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I own BT 4 Deluxe Edition on GOG, I started playing it on Xbox Gamepass, and it had Achievements.

Sadly, I only noticed that the GOG version doesn't have achievements after I bought it.
However, it's on sale on Steam, so I was wondering if the Codes I got with the GOG Deluxe Edition, can be input into the Steam Standard Edition to unlock the extra items?
This is really (and I mean REALLY) late, but no, GOG codes do not work with steam, and vice versa. The only thing that's set up, and has been mostly abandoned, is GOG Connect, where GOG eats the cost and lets you have GOG copies of your steam games in certain instances if you link your steam account.

This was really big a few years ago, but I think with development costs of CP2077, and subsequent results after launch, it's fallen by the wayside. The last few sales I haven't noticed any games posting to Connect.

Hope this helps, sorry I didn't give good news, and even more sorry nobody answered this sooner!

-Timbro