The pictures are stored in the Photos Library, and that's what you have on your external drive, right? This library can be read by any Photos app from the same or newer OS. BUT, for a newer OS, Photos will re-write its database to take advantage of new features. That means that once you use, say, Ventura, to read the Catalina library, then Catalina will no longer be able to access it, since Catalina doesn't know about the new database.
The Unmodified Originals in the library will always be unmodified-- they can be exported unchanged to Finder anytime. Edits and keywords that you have added will also be intact when you export edited copies. Photos doesn't store edited pictures-- its database stores a record of the adjustments that were made, and it applies those on the fly when you look at them. Really, the pictures will all be the same. Not to worry!
That said, if I were you, I would make a copy (option -drag) of the library in a separate folder. Backups relieve a lot of tension. Then you just plug in the external drive and double click on the library.
Also, keep in mind: To get full functionality (and to avoid damaging the Photos Library) an external drive must be formatted in either APFS format or Mac OS Extended (Journaled) format. Additionally, the drive can not have had Time Machine on it since it was formatted.
Move your Photos library to save space on your Mac - Apple Support
You may have gotten away with a non-Mac format in the past, but it would cause lots of trouble in the future. We've seen lots of that.
We upgrade to new OSs all the time-- it works.
