Thank you all for commenting here, looks like I've found the solution.
Make sure to remove all the users' access to the app you are going to transfer on the Users and Access page (https://appstoreconnect.apple.com/access/users).
Open https://appstoreconnect.apple.com/access/users
Filter by the app that you're going to transfer
Look for users that have access to the app (other than users with "All Apps" access)
Remove the access to this app for such users.
Note: admins and other users that have "All Apps" access may retain their access to the app that you're transferring.
Note 2: Don't forget to expire all the TestFlight builds and delete all the Test Groups in Testflight.
After that, try initiating the app transfer process once again.
Good luck!
artem2507
Users receive reputation points by contributing quality content to the forums.
Posts include post and replies published on the forums.
Post authors can mark replies as Accepted to indicate successful solutions.
Apple Developer Forums admins can mark replies as Apple Recommended to indicate an approved solution