Notably there were a lot of issues related to loading saves mid-mission which caused missions to break.

On the product homepage they say that it has been modified to run smoothly on modern OS and support cloud-saves now, but they are very vague with no specifics:

https://www.gog.com/game/alpha_protocol

I'm really curious too especially because i actually got the last DVD release of Alpha Protocol working in Windows 10. This is the final Sega patch release where they removed DRM. I played a tiny bit using the mouse and keyboard and it seemed OK but i didn't get far into the game. Is gameplay better with a game controller?

In my case it won't even start. So at least that one bug is something that I can confirm still exists.

Would be good to get more details on what was changed to make the game "run smoothly on modern OS[s]"?

I find that with many GOG "historical" releases, I still have to apply additional patches to improve QoL and having things run more smoothly.