Each password is stored encrypted, with AES-256-GCM and a key derived for each project, and the server uses it to run the project's hosting and database operations; it gives it to no agent, and shows it only to the project owner or a manager who asks with an email code.
When you type a password in the app it goes straight to the server: your PC keeps no copy, and the hosting and database settings of a project are the same for the owner and every manager. On a new PC you do not type those passwords again: you sign in and the server already has them.
The test before saving catches a wrong password only when it can finish; if it cannot, SyncNow saves a hosting password anyway and asks you before saving a database one. If a stored password stops working, the project's row shows a yellow sign when SyncNow sees the hosting or the database refuse it; to see a stored one, read Can I see a password I already stored in SyncNow?.