Why do I need to start ssh-agent twice?

Question

I'm on a Raspberry running Raspbian GNU/Linux 11 (bullseye). Im stuck with a strange behaviour. After booting, ps -ef | grep ssh says

    root       482     1  0 16:03 ?        00:00:00 sshd: /usr/sbin/sshd -D [listener] 0 of 10-100 startups
    pi         605   555  0 16:04 ?        00:00:00 /usr/bin/ssh-agent x-session-manager
    pi         724     1  0 16:04 ?        00:00:00 /usr/bin/ssh-agent -s
    root       780   482  0 16:04 ?        00:00:00 sshd: pi [priv]
    pi         795   780  0 16:04 ?        00:00:00 sshd: pi@pts/0
    pi        1038   796  0 16:06 pts/0    00:00:00 grep --color=auto ssh

If I enter ssh-add ~/.ssh/id_rsa I receive Could not open a connection to your authentication agent. Same if I use sudo.

As read from other discussions I enter eval ssh-agent -s and then I am able to do ssh-add, but now I have ssh-agent twice in memory:

    root       482     1  0 16:03 ?        00:00:00 sshd: /usr/sbin/sshd -D [listener] 0 of 10-100 startups
    pi         605   555  0 16:04 ?        00:00:00 /usr/bin/ssh-agent x-session-manager
    pi         724     1  0 16:04 ?        00:00:00 /usr/bin/ssh-agent -s
    root       780   482  0 16:04 ?        00:00:00 sshd: pi [priv]
    pi         795   780  0 16:04 ?        00:00:00 sshd: pi@pts/0
    pi        1048     1  0 16:10 ?        00:00:00 ssh-agent -s
    pi        1050   796  0 16:11 pts/0    00:00:00 grep --color=auto ssh`

• What starts the first agent? I've looked for .bashrc and .profile, but there no agent is started.
• Why can't I connect to the first agent, although both are started by pi?
• Does it matter to have the agent twice in memory? Is it good, is it bad?

Thanks for any help