Living vs dead dna, how much of a difference is there in their stability? I figured it's the replication process that's prone to mutability.

Either way, that's nothing we can't solve with ECC. At >200 petabytes a gram, we can easily sacrifice half of that storage for redundancy and error correction bits and it's still pretty damn dense.

Dead DNA suffers from degradation as well. Being an organic substance, quite a bit actually.
And how would we store the DNA material? Some super-advanced material or organic suspension that we find later wasn't enough to protect against various radiation or viral / bacterial / prion infection?

I save all my data in Tupperware containers.

I never liked to use CDs, DVDs and such as a storage. I always saved my stuff on hard drives or zip drives (those weren't the most popular things). I still have data saved on 5 hard drives that I bought early 2000, and they are still working.

Total energy of the universe is a constant, and total entropy of the universe is always increasing.

The universe is expanding forever, therefore, so long as the universe is expanding, the entropy capacity will increase and it will increase at a faster pace than the universe's actual entropy can increase, and the maximum entropic capacity is thus also forever. Also, random quantum fluctuations can occur in an otherwise completely empty space, so the universe will never be "hot" enough to erase all information.

Simplest explanation; the warmth from a flame will dissipate and spread endlessly in an -35 Celsius environment, but for all purposes, it will be -35 again after awhile when the flame is gone.

This means also that the information IS intact because of quantum strings... and then frozen by the goods to be probed, extracted, analysed and perversely misused. :P

I mean they're sequencing DNA that's claimed to be anywhere from a hundred thousand to >million years old. Permafrost seems to work well enough for preservation, but I think the scientists in their labs have ways to preserve it too.

Stone sculpting.
Rosetta stone is still here, piramids also, mount Rushmore will be there until the end of the time.
Can't almost go wrong with stone.

Incomplete sequences. Degraded samples.
And there is a difference between the blind luck of perfect / near-perfect preservation conditions vs the success of intentional preservation.

Inorganic outlasts organic hands-down.

EDIT:
(Warning: Incoherent and rambling discussion below)
Of course all this discussion is somewhat ridiculous. Languages are lost / forever altered, data formats / encoding become obsolete. The longer that time passes, the more likely that complex recorded data become unintelligible to future generations.

Unless you can find a way of ensuring that data can be understood long after it is written, you're wasting your time preserving it that long.

Stargate SG-1: The Torment of Tantalus (I know, sci-fi, but we are edging on the fantastic anyway) discussed somewhat the difficulty of preserving important information of a civilisation long-term without a language barrier. Even if you manage to create a way to make something last long enough, it doesn't guarantee that whoever or whatever finds it will comprehend what it means (assuming a similar intelligence and technological level). I mean what are you going to do, encode the instruction manual for how to read data in the same format as the data itself? This would as pointless as having the book "How to read French" published in French.

Do we truly need to attempt preserving anything that long in the first place? Anything of serious relevance to current generations can be recorded in more conventional means.

I can imagine a caveman involved in a accident with a fire pit scrawling on the cave wall his final words of wisdom that modern man would find today. Years of research scouring caves to attempt to understand the drawings, thousands/millions of dollars spent on the endeavour, finally the message gets a rough translation: Fire Hot.
I can also imagine a future evolved human discovering (let's say for argument) a perfectly-preserved M-Disc, the only one of thousands found intact. Disc analysed, data eventually decoded. The contents: pirated episodes of Keeping Up with the Kardashians. XD

Addressing the claims of the longevity of M-Disc. In even 100 years we probably won't have the hardware around capable of reading the disc in the first place. And even if we did, chances are the software on it will be incompatible to use. The best you can expect of such claims is only this: The disc/data will remain usable until it is useless to own it (which is a lot shorter than its predicted lifespan). And this is the ultimate end with all media and games, unless it is modified into new forms and re-recorded onto new storage media, it will die.

I wouldn't be so sure. In all likelihood, such optical drives will become obsolete (I'd say they already kinda are since most computing devices don't have optical drives and things like usb flash & cloud storage excel in convenience). But I'm not sure they won't be around. New CD drives are still being made even though the tech is 36 years old. Turns out CDs are hugely popular, and perfectly adequate for music at least. People have huge collections, so there's a demand for compatible devices. 3.5 inch floppies are around the same age, you can still buy new floppy drives, even though floppies have been obsoleted by CDs. Now 5.25 inch floppy drives are hard to come by, but they weren't exactly a commodity back in their day.. computers weren't a commodity! NES & SNES cartridges are rather obsolete and we can play the games just fine thru emulators. Dos software is obsolete but again dosbox & emulators.. Software is arguably the hard part, and we can still manage.

Other media is much easier. It's not like video codecs would just vanish, right? It's not like PCM audio would stop making sense.

Hard drive prices haven't fallen as much as they once did and SSD are faster but not as good for long term storage.

Has anyone else brought up 5D optical data storage?

Up to 360 terabytes stored permanently for billions of years, resistant to 1000 degrees celsius, on a single piece of fused quartz no bigger than a coin.

I'll take this over something as potentially unstable as DNA.

How "long term" are you talking about?

"While it is true that SSDs wear out over time (each cell in a flash-memory bank can be written to and erased a limited number of times), thanks to TRIM command technology that dynamically optimizes these read/write cycles, you're more likely to discard the system for obsolescence (after six years or so) before you start running into read/write errors with an SSD."

And then there's this:

"An SSD has no moving parts, so it is more likely to keep your data safe in the event you drop your laptop bag or your system gets shaken while it's operating. Most hard drives park their read/write heads when the system is off, but they are flying over the drive platter at a distance of a few nanometers when they are in operation. Besides, even parking brakes have limits. If you're rough on your equipment, an SSD is recommended."

https://www.pcmag.com/article/297758/ssd-vs-hdd-whats-the-difference

but how long does the information stay usable on a SSD compared to a hard drive disc.

25 days
You wanted an easy answer, ignoring any variables, right?

People confuse data retention (constant gradual cell charge leakage) with endurance (SSD rewrites before death) but they're not the same thing. Flash cell leakage is all part of the technology and has been a thing for years with many people burned by putting wedding photo's on a flash drive throwing it in a drawer then 5-6 years later finding it's corrupted (or even empty - everything gone including the file system and partition structure).

If it's powered up (eg, system drive booted each day), an SSD's controller will transparently refresh the data in the background indefinitely until the drive fails as and when it detects cell charge degradation. But obviously if it's unpowered it can't, and under those conditions data is then guaranteed for a maximum 1 year unpowered on SSD's (JEDEC standard). SSD's trump HDD's for system drives, but HDD's still win by a long shot for "cold storage" (data longevity of drives continually unpowered for years).

Edit : I think the general rule of thumb was something like - in a continually unpowered state, SSD's have 15-50% electrical cell-leakage per year depending on a lot of factors including cell node size - the larger (older) the better, the smaller (newer) the worse, and the difference in SSD tech SLC (best overhead) vs MLC (average overhead) vs TLC (least overhead). But HDD's only typically lose between 2-5% electro-magnetic field strength per year (assuming they're stored away from strong electro-magnets).

That's nice but you've fallen foul of your criticism by failing to specify what planets days you're talking about.