This is a stressful situation, but the fact that your iPhone Storage still shows 376 MB used by Notes is a very good sign — it means the database is still on your device, just not being indexed by the app. Here are the steps to recover them:
1. Check the "Recently Deleted" folder — In the Notes app, tap the back arrow (<) in the top left until you reach the "Folders" list. Look for a "Recently Deleted" folder. If it's there, you can recover your notes from it.
2. Force restart your iPhone — This can trigger a re-indexing of the local databases. Press and quickly release Volume Up, then Volume Down, then press and hold the Side button until the Apple logo appears.
3. Re-verify account settings — Even though you don't use iCloud Notes, signing in and out of Apple IDs can sometimes toggle local storage settings. Go to Settings > Notes and make sure the "'On My iPhone' Account" toggle is ON.
4. Check your "Other" Apple ID — You mentioned signing into a different Apple ID temporarily. It's possible the notes were moved or associated with that account's local cache during the swap. Try signing back into that "other" account temporarily just to see if the notes reappear. If they do, copy/paste them into a temporary document or email them to yourself.
5. Restore from a local backup — Since you don't use iCloud, your only other recovery option is a full iPhone backup made to a Mac or PC *before* this happened. You can restore your iPhone from that backup to get the notes back, though this will also revert other data to that point in time.
6. Offload and Reinstall the Notes app — This is a safer way to reset the app without deleting its data. Go to Settings > General > iPhone Storage > Notes > tap "Offload App". Once done, tap "Reinstall App". This often fixes database connection issues without wiping the 376 MB of data you still see.
DO NOT "Delete App" as that will permanently wipe the 376 MB of data. Try the "Offload" method first.
Hope this helps you get your notes back!