Right- and left-clicking the face that "should" be the front works as normal, and it does retain items, but it appears to be always empty and facing north. Exiting and re-entering the world will cause drawers to appear correctly, but only until I try to put more items in them.
https://imgur.com/a/JH1AE8M
Storage Drawers 1.12.2-5.3.8
Forge 14.23.5.2844

I have a similar issue, with the drawers appearing to lose their items when adding more. However, my drawers didn't rotate, and I also did not have any Storage Drawers extension mods. The conflicting mod in my case was Millenaire Extension. Hopefully this info is helpful!

I got the Same Issue and it seems related to Storage Drawers Extras, though I also had Compact Drawers.
Removing both fixed the issue in my modified Enigmatica 2 Expert instance.
I grabbed the following error log from the Problem:
https://pastebin.com/JUvDppBr
From my observations it seems that the slot counts get out of sync somehow, especially with the 2x2 drawers, as when shift rightclicking them my whole inventory gets shifted around, but when resyncing everything is back at its old place. I was using Drawers from Storage Drawers Extras, because I just happened to have wood supported by that mod.

I have this issue, and I'm not using Extras. So it seems that SD Unlimited is the cause of this issue.

The client-side TileEntity is surely getting lost, but I still don't know how. Thanks for the extra data point though.

Is there anything else "interesting" in that area? How heavy is your mod pack?

I had the same issue, it was fixed by removing the Storage Drawers Extras and Storage Drawers Unlimited mods.

Same issue here. It's also worth noting that framed drawers also lose the textures from whatever I'd made them from, and drawers from the Extras mod (which I'm bringing up since you also made it) just flat-out don't work properly at all, turning "my texture is missing" hot-pink or just outright not rendering whatsoever. I didn't test any drawers from Unlimited, and even if I did, it probably wouldn't be relevant to bring up, since you're not the author of that one.

I am using the latest versions of all required mods, and for the record, the modpack I'm playing in is a modified version of Enigmatica 2. It seems like a compatibility issue with either Extras, Unlimited, or both- removing the mods fixed the issue for me. I didn't test with Unlimited alone or Extras alone, but I know one of the two is causing the issue.