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Makes sense. I would've thought that part of the description would mean the slot could under such circumstances be refilled before it disappeared and not lost.

More specifically to the point, it would need a different name entirely because the actual "burnout" as recorded is the named event that is reflected in the message log when that occurs. Don't really want to introduce another term, though.

Yep, that is exactly what it records, the number of propulsion actually lost to it, not integrity damage. It could potentially be switched, since actual complete burnouts are quite rare, but it's not a bug and not yet on my list (we were actually having this discussion earlier this week).

Yeah that's a possibility, this is normal behavior. As you might be familiar "Burn" is a special critical that specifically requires Heat Transfer to operate, but your weapon currently has no base heat transfer capability at all, so the critical will not show since it doesn't currently apply. Technically it has that chance after the modification, but it won't show.

Oh, i should probably link to relevant scoresheets.
With 207 overloaded moves but no burnout : https://cogmind-api.gridsagegames.com/scoresheets/J4TTp7kEzZzh5e6H
With 34 overloaded moves, and 1 burnout count : https://cogmind-api.gridsagegames.com/scoresheets/uEJvMnwyA9RZLvJac

The bad ones are really bad but the good ones can be lifesavers.

Yes very specifically the Storage Unit swapping rules were actually changed for a short period during Beta 13 development to make sure that doesn't happen, but it actually lead to even more problems for players, so was switched back

Specifically with Storage Units you're going to have to be more specifically aware of which ones you want to keep, and do this manually rather than relying on the automated system if it won't suit your needs. But making a special exception for those does lead to even more issues for the majority of players in the majority of situations, as we discovered through actual experience with the alternatives earlier this year in testing.

There won't be warnings added for this particular feature, you'll have to swap manually if you don't want automated behavior, which has very few rules and is quite consistent for the very reason that it's easy to predict what will happen if you let the automated system do its thing.

(The system is getting expanded even further in Beta 14 to allow manual ground-attached swapping when the automated system will otherwise do nothing, but that's a different issue.)

Yeah that's not a bug, just the way things are. SE can create things in temp slots, but you're going to lose them all the same when the slot is gone, but as described on the part, sometimes a temp slot may require an extra bit of time before it really disappears because it's no longer supported. Best to just keep SE off if you're about to have an unstable situation, so that it doesn't produce anything under poor circumstances, or keep going and have it build something else after the fact... Temp slots are unstable by their nature.

Maybe it's intentional, but just in case, the "Propulsion Burnouts" scoresheet entry seems like it counts the number of parts destroyed due to burnout, even though it feels like it should count the amount of times burnout took out integrity from propulsion units.

That's a surprise to me! That run, my first W++, had just about the worst seed (FluxMiningMachine) i ever encountered in terms of prototype/AA stashes and other random run-changing stuff from branches. I also made several pretty big mistakes that affected the extended game portion of my run, and bad luck with the layout of the second-to-last area.
And i still won, with exactly 400 core integrity left and 3% core exposure. The only time my build started falling apart was right after getting the second +, and even if it had started to fall apart sooner i'd have managed to get said +.

Here's every part where i had bad luck from the seed FluxMiningMachine and the few parts where i had good luck (Spoilers for extended game and a lot of branches) :

Spoiler (click to show/hide)

Mines : Bomb Drone Bay, was pretty useful.
Exiles : Deserted, the remaining Prototype was Army-in-a-Box, which was going to be largely useless for a flight run and not worth the six slots.

Lower Caves and their respective branches : No A8 code, Megawrench and some derelict allies (both pretty useless on flight), Core Expander (weapon, which even if it still ended up being useful, was the worst slot type to get).

Warlord : Experimental Cloaking Device, which was nice, but no hackware or Spectral Analyzer.
Zhirov : Dissipator, no propulsion (none useful, at least), no hackware.

Quarantine : The place where all the good luck went. Seriously, aside from Cryocooling Ducts not being there, every single possible AA was there.
Testing : Disintegrator and Shell Armor, no other special prototypes.

Section 7 : 2 Integrated Mediators, 2 Microwarp Drives, 2 LRC Insulators, 1 Integrated Reactor and 4 Integrity Redistributors. No S7 Guards or AAs. Used the Subatomic Replicator on the Integrated Reactor.
Command : Weapons were Graviton Cannons and Enh. Nova Cannons (really?), useful non-guaranteed stuff were Exp. EM Disruption Field, Exp. Phase Shifter that i couldn't support with the rest of my build, and Gamma Refractor.

A0 : Dissipator, Mediator (oh come on!). One stash of Ionic Axes that were very useful.