Whenever I try to steamroll a weakened unit with a tank I get the 'fire' sound 2-3 times and then the game crashes to the desktop. I used to have the same issue with the original game back in the day and had not expected to have to deal with it again.

Is there a solution to this?

Does this happen independent if the tank moved before or not? (Panzer General 2 had an underflow bug: if a tank disembarked, it had 0 movement points but could still fire which would remove the movement by one and it got many movement points, maybe 99)

Hadn't the issue with the old version and not with GOG's one. Is a custom codec for playing .wav files installed?

I was only able to reproduce the mistake after moving the respective tank unit. I move the tank to a very weak enemy unit, the unit gets steamrolled and then the game crashes.

If the folder 'Wavs' in the installation directory gets renamed to 'Wavs-disabed', does the crash still occur (sound won't work except the one on launch)?

Nope.
I was finally able to try this, but the same mistake as always. My tank faces a weak enemy unit, the enemy unit gets crushed and then the game crashes as well. To the desktop.

It's very strange you hit the issue 25 years apart. Did the GOG version get installed into a different folder (in case you had the previous version also on the drive) and is this the one which actually get launched? Attempts to reproduce the issue fail here: Launched the Western Campaign, move the infantry north which discovers and fights the BRDM-2 AT. Attack it with artillery (Paladin) and it might be ready to get overrun by a tank, else I tried it with the BTR-80 further north and heli + tank.