Your concern is very valid — moving from a 2013 iMac to a 2024 iMac with macOS Sequoia will be a big leap, not so much for the OS itself, but for the app versions and file formats involved. The good news is that both Photos and Pages are designed to migrate your existing libraries and documents forward, but there are a few things you should prepare for to ensure you don’t lose a single image or formatting detail.
For Photos
Your existing Photos (or iPhoto, if you haven’t upgraded that library yet) library will need to be converted when opened on the new iMac. This is handled automatically by Photos on first launch, but the conversion process can take a while with 65,000+ images. As long as you copy the entire Photos Library package from your old iMac to the new one before opening it, all metadata (albums, edits, keywords, etc.) should remain intact. I highly recommend making a full Time Machine or Carbon Copy Cloner backup of your old iMac before you start — that way, if the migration hiccups, you still have your untouched original library.
For Pages
Documents made in older versions of Pages will open in the latest version, but if they’re very old (Pages '09 or earlier), certain formatting elements might shift slightly because Apple has changed the underlying file architecture over the years. Most text and images come across fine, but complex layouts — especially newsletter-style designs — should be reviewed after migration. If you want a bulletproof fallback, export your most important projects to PDF from the old iMac before moving them. This ensures you’ll always have an exact replica, even if the editable version changes.