First let me recap the situation as I understand it:

1. Achievements aren't part of the base game. They're added by Deus Ex Revision, a free DLC.

2. You start Deus Ex Revision by clicking the More button to the right of the Play button for Deus Ex GOTY Edition, and choosing Additional Executables, then Deus Ex Revision.

3. You don't see any achievement notifications because the overlay isn't supported by either the base game or the DLC.

4. If you do unlock an achievement, in GOG Galaxy you can go to the Activity section under the Friends category. There you can click the Deus Ex Revision icon, which opens up the usual details page for a game. From there you can click My Progress at the top, then the Bookmark icon to the left of that.
Achievements also show on your profile page on the website, for Deus Ex Revision.

And now the part that I find puzzling:

GOG Galaxy lists achievements for both, but nothing under Deus Ex GOTY Edition unlocks. On top of that, a lot of icons are missing for regular (not secret) achievements, which isn't the case for Deus Ex Revision. See the attached screenshots.
Does anyone know what's going on? I'm tempted to open a support ticket, but given my previous experience, I'm convinced that would be pointless. Also, someone already did that a year ago, and unsurprisingly nothing is fixed.

Update: achievements are completely borked. I tested 3 achievements. It went like this:
- "Off to a Great Start" shows for Deus Ex Revision both on the site and in GOG Galaxy. The global stat for it incorrectly says Legendary 0.0%. For that matter, that's what it says for all of them.
- "Don't Let it Go To Your Head" only shows on my site Profile and Activity Feed pages. It appears locked on both the achievements details page and GOG Galaxy.
- "All I Have is a Candybar" ridiculously shows as "Secret achievement" on my own Profile and Activity Feed pages. Same as above, it appears locked on both the achievements details page and GOG Galaxy.

I went ahead and opened support ticket #1151556. I don't expect anything will come of it apart from more frustration that problems aren't fixed. But I'd like to be pleasently surprised.

Update no. 2:
+ After a long delay, the achievements showed up on my profile page and the details page. I can now see the "secret achievement" on my own profile.
+ After an even longer delay, the achievements eventually showed up in GOG Galaxy as well.

- Stats tracking is still broken; every achievement is Legendary 0.0%
- It's still confusing that Deus Ex GOTY Edition shows achievements as well, but none of them unlock and most are missing icons.
- It's still confusing that there's no obvious way to track the achievements for Deus Ex Revision in GOG Galaxy; you have to go through the Activity section to find it as a separate entry from the base game and get to the achievements that way.

Edit: maybe it's also worth noting that play time for Deus Ex Revision stays at N/A because it gets added to Deus Ex GOTY Edition. I think that's normal and that's how it should work with the achievements as well.