You should only have one EndNote Library. Multiple libraries inevitably means confusion with where references are saved, duplication and mistakes. However, you can have the same EndNote Library available on more than one device, and to do this, you need to 'sync' your EndNote 2025 Library with EndNote Web. Syncing with EndNote Web also:
If you have previously used EndNote Online/Basic and wish to start using EndNote Desktop, syncing will get all of your existing references into your new EndNote desktop library.
If you wish to sync your accounts, you do this within EndNote desktop: