I read somewhere that in turn-based mode, recovery time doesn't matter, people just take turns based on their Speed stat.

Is that really the case? This would make Mastering skills a lot less useful, since for 95% of offensive spells, the only benefit between Normal/Expert/Master is faster recovery. Has anyone tested this?

I'd say recovery time doesn't matter as much but it still matters, this is most obvious when you have blasters going

Basing on my observation, I would tell that recovery has some impact on turn-based mode. Example of my Arch-mage - after reaching master skill in Fire and Water I was capable of using spells twice instead of once per turn (before enemy units are attacking). But I admit that at the same time I was also paying attention to give all my characters some items with bonus to speed, so I would say that it was generally result of combined speed and decreased recovery time.

Most spells give bonuses per skill level, so if you want to be effective you need to put skill points into it. I think all spell schools have some important benefit from increasing your mastery level just from utility spells alone (fly/TP/Lloyd's etc). Anyway, if you put skill points into a spell school in order to become more effective, then after skill level 10+, all that separates a novice from master is like 7k gold.

Regarding recovery in turn based mode:
I just tested my monk with and without haste. Vs 1 goblin, I'd get off 1-2 shots before it was his move (2 shots probably 70% of the time ish), but never 3 shots.
With haste, I get 2-3 shots between every time he moves (3 shots about 50% of the time).
So based on this very limited testing, recovery time has value in turn based mode.

Maybe the speed stat only matters when determining how early you take your turn (i.e. if fighting 5 goblins, they all get to swing before you if their speed stat is higher).

A higher speed stat improves your recovery time. Turn based just slows down how fast time passes, effectively pausing time when one of your characters has a turn. The better a character's recovery time, the sooner they are ready to act again after taking an action.

The Knight or Paladin Class are the only times I have noticed it and that when they are only Level 1-3 Armor.
To me the trouble is "Speed" seems to mean more or the two blend together

In turn-based mode, faster recovery means more turns. Very obvious, and important, if you have somebody using a dagger when others have swords or maces.

The "Speed" stat, by the way, makes minimal difference to recovery time (with weapons and bows - spells are something else again, so with regard to them I just don't know); it is Armor Class that Speed is good for.

As said before. Recovery time matter a lot for both turn-based and real-time.

Recovery time is the important stat while speed just give you a marginal decrease in recovery time with ever diminishing returns, as your speed stat gets higher. (Speed also adds some to your armor class.)

The only time the speed stat matters much is in the beginning of the game. Going from 7 to 50 in speed gives you -12 to recovery time which is around half the effect of "haste" (-25).

This page explains some mechanics that the game and manual was vague about in an easy to understand way:
https://grayface.github.io/mm/mechanics/