Strange, I'm currently out of ideas. I tried on my old Intel machine, but even there it is loading fast (it feels like it appears instantly when hitting my keyboard shortcut).
Maybe something got corrupted somehow at the database level. Maybe you could try to temporarily move the database files to some other location (while BTT is quit) and see how it behaves with a fresh database.
~/Library/Application Support/BetterTouchTool/BTTClipboardManager_20241210.sqlite
~/Library/Application Support/BetterTouchTool/BTTClipboardManager_20241210.sqlite-shm
~/Library/Application Support/BetterTouchTool/BTTClipboardManager_20241210.sqlite-wal