It's really important for you to get a better understanding on how Google has been gradually changing its Google Photos into a much more proprietary, vendor-locking service. Your expectations that terms like 'Sync' have been redefined to match up with Google's current business plan. So when you use the Google Photos app, you'll be viewing your library of photos and videos BUT the actual photo and/or video files themselves may or may not actually reside within your phone's internal storage media. That's the big issue. They may or may not be on your phone, but they are all stored within your online Google account.
Using the Google Photos app on your phone will show you your entire photo/video library, a merged collection of media files both stored on your phone and on Google's online servers. But if you use a file manager app on your phone, that's only going to show you the photo and video files that are stored on your phone.
-- You can get around this by tweaking options in the Google Photos app on your phone, but that will only affect your Google Photos service going forward, it will not apply retro-actively. (Change
Backup quality to
Original and stay clear of that
Free up device storage option.)
If you do want to have your entire photo and video library stored within both your phone and in your Google account, it's going to be a bit of a messy project. Using just Google Photos (using either the app on your phone or its web interface) will very, very time and effort consuming. So a workaround is to use the Google Takeout service to make a single, downloadable zip file of your entire collection.
Log into your Google account, deselect all the shown categories except Google Photos, and then depending on your large your media file library is it might take a while before you get a finished message with a link to download the zip archive file. De-compress that zip onto your phone and it that will restore all the photos and videos that were in your online Google Photos account. (Note at that point you'll have a messy mix of duplicates, the existing photos/videos that were already on your phone with those recently downloaded files.)
-- On related topic, using Google Takeout is a good way to make a backup of your entire Google account into a single file. And it can use user accessible file types so that's a major plus. It's also a good way to get a grip on just how extensive Google is about storing our personal files and such.
If you've been using Google for several years, don't be surprised how long it takes to do a Google Takeout backup file (could be several hours and the zip file itself several GBs in size).
If your seeing old backups of your photos and videos in your Google Drive service, for several years the Google Photos service and the Google Drive service could be linked to automatically sync your media files between each service. But Google killed that off in 2019 in its push to vendor-lock users to Google Photos.
What’s changing Starting on July 10, 2019, Google Photos will no longer sync to Google Drive. From that date forward, if you add or delete f...
workspaceupdates.googleblog.com
Regarding your old text messages, don't spend too much time trying to find a solution. The odds are those are lost forever, unless you still have that Galaxy S21 phone. Trying to restore old text messages from old backup files is pointless, you can't restore data that doesn't exist.
However, if you do still have possession of that Galaxy S21 (not a backup file but the phone itself), install this SMS Backup & Restore app on both phones, use it make a export a backup file of your text messages (and phone call log if necessary), and the use the app to import that backup file into your Galaxy S23 phone.
A simple app that backs up and restores SMS & MMS messages and call logs.
play.google.com