Yep, been having the exact same bug/lag issues on Classic Era – Whitemane – Horde.
Just posted about it in the WoW Classic Patch 1.14.4 Known Issues List - 08/22/23 thread, as I was surprised it hadn’t been mentioned there yet.
Personally, I had the same auction house issue that you did, and I was experiencing similar lag when trying to get mail from the mailbox. Seems like there are lag issues all throughout the game after the patch.