not keeping sessions

Hello,
I copy my site to a new server with the same domain name and just switch the domain name of the original server.
Now the old server is still working fine with the new domain name, but the migrated content with the original domain name has a session issue.
I can see the login happens, but the user is logged out instantaneously.
It's happening with the admin and all other accounts. I can create new account, but the same issue happening to the newly created user.
I am copied over the same database with same names and credentials.

original contents under new url is **redacted**
migrated contents under original url is **redacted**

Feel free to create new user on both and see if you can help me understand what is going.

thank you.