First, how is your external drive formatted? To avoid damaging the Photos Library an external drive must be formatted in either APFS format or Mac OS Extended (Journaled) format. There have been so many problems with using incompatible drives that the newest macOSs won't even allow a Library on a non-Mac formatted drive to open, since there is a chance of damaging the Photos database. See this:
Move your Photos library to save space on your Mac - Apple Support
If this drive is in a an incompatible format, stop running Photos with it immediately! A Photos Library can sit on an incompatible drive, but running it may corrupt the database.
If your drive is properly formatted, then we need to figure out what you're saying. You mention Photos, iPhoto, and "my I photo library." You say you're using macOS 15.4 Sequoia, so I'm guessing that you're meaning Photos, since iPhoto is an app that was discontinued 10 years ago, though some people still have iPhoto Libraries.
It sounds like you have more than one Library-- is that right? You can see a list of your Libraries by closing Photos and option-clicking on the Photos icon to bring up the Library Chooser. What do you find there?
How are you opening Photos? How are you deleting Pictures?
Are you using iCloud Photos? Do you use Optimize Storage with iCloud Photos?
Give us more clear information so we can help…