We finally got this resolved with support about 6+ weeks. The issue is that App Volumes 2512 is trying to sync app links using the API endpoint /app_volumes/app_links/update_batch which App Volumes 2503 does not have. The error we saw:

Application <name> not synced to Manager Instance machine: [<target>] because App Product sync has exceeded maximum number of attempts. Ensure the target ["<target>"] is configured properly.

Upgrading the source instance to 2512 resolves the issue. This doesn't appear to be documented anywhere.