On multiple instances I've been tabbed out of playing something by a password dialogue asking for my admin password to apply an update, and it usually doesn't take the first no for an answer. And telling it no seems to reset the update back to the beginning.

Even if I launch something from another store through Galaxy 2.0 it still tries to update Galaxy games. Is there anyway to tell Galaxy to not even try updating if I'm playing something?

no and its a pain in the ass but the dev team didn't test things so this senario didn't come up

Settings -> Installing, updating -> Pause downloads when playing

This should prevent Galaxy from downloading/installing updates while you're playing.

I have that option ticked, and it does work for Galaxy games, but it doesn't seem to be applied when playing something from another store even if was launched through Galaxy.

Well yeah, Galaxy only controls updates from its own ecosystem. Update behavior for non-Galaxy games has to be set in their respective clients

the games are launched from Galaxy... that's the point!
so Galaxy has to have an option to disable downloads and that is easy to code... as I said, the dev team just didn't think of it

If it is "easy" to implement depends on the APIs of the other clients. If there is no means to tell Epic, Steam et al to keep their update mechanism on low profile, then it is almost not possible. You are demanding to alter the settings in another software, or even its code.
Main Problem is: You tell Galaxy to Launch game X, to launch it the respective launcher is started and with that its settings come to be active. If the launcher has auto update, also during game sessions, set... Well, that's what will happen, it is a setting in that launcher. If it doesn't offer APIs to alter its settings from outside, bad luck. But also that is not a problem with Galaxy then.

Easiest solution would be to setup all clients to your wishes after install and Galaxy will launch it with those settings.

Is that your professional opinion as a software developer with particular expertise in digital distribution clients?

I do not think that is what he/she means:
There is no need to change the other clients as the games is started through Galaxy, so Galaxy already knows that the "external" game is running. It just does not do anything with that information currently, in contrast to games from gog.
As for resuming, there must also be a mechanism already in place to detect when a games is closed, or if not it should not be too hard to scan the list of running processes for the process-id of the game.

correct, the issue here is Galaxy downloads during play, not what other clients do

yes galaxy does know the other games are in play because it started them... the ui already tracks the fact that a linked game is running [look how your play button changes colour] + another option is to manually pause galaxy downloads [auto is best but manual option will at least work]

Gog needs to fix this or they can forget about Galaxy 2 because playing 3rd games is the main selling point of having this new ui

Okay, now I think I get what you want. It sounded like external games were updating (sp?) when you start an external game, respectivly the launcher is started. This would be hard to stop, since it is the external launcehrs setting.
You want "internal" GOG games to stop updating if an external game is launched? Okay, for this there should be a flag, or rather could. Galaxy really knows the game is running.

Perhaps the devs never thought it to be a use case? Actually due to the slower internet speed around I enabled downloading while playing, after noticing nothing happened if I was playing a game (to bridge the download time. D'Oh!)