ssh_agent problem on 2nd sessions

Distribution

mint 22 and mint 22.1 beta

Package version

cinnamon 6.4.2 and 6.2.9

Graphics hardware in use

No response

Frequency

Always

Bug description

not sure this issue is related to cinnamon, may be a problem of ssh-agent...
this is the same issue posted at : https://github.com/linuxmint/linuxmint/issues/705

i repost it since it is still here in LM 22.1 beta.

after logout and login again with the same user, the ssh-agent is running, but SSH_AUTH_SOCK env is not set
thus ssh-add say : "could not open a connection to your authentication agent"

Steps to reproduce

login into cinnamon session, launch ssh-add -L in a terminal

• it display the ssh-key identities of the user
  logout and login again with the same user, relaunch ssh-add -L in a terminal
• it says : could not open a connection to your authentication agent

Expected behavior

ssh-agent should work in every cinnamon session, not just the 1st one.

Additional information

this is a repost of https://github.com/linuxmint/linuxmint/issues/705

No files or tests are named. Reproduce the issue with ssh-add -L before and after logging out and back into the Cinnamon session, then compare whether SSH_AUTH_SOCK is set; done when ssh-agent works in every Cinnamon session.