SSH does not use pubkey even though correctly setup

I'm trying to setup my pubkey, and it works fine, except the first connection of the day, that keeps on asking for the password explicitly.

It's not a major problem for me, however I would love to create some services that would connect to that server, and that password request I'm afraid would break everything.

If i run ssh -vv ... during the connection when it asks for the password, I get:

OpenSSH_9.8p1, LibreSSL 3.3.6debug1: Reading configuration data /Users/my_username/.ssh/configdebug1: /Users/my_username/.ssh/config line 79: Applying options for acquario3debug1: Reading configuration data /etc/ssh/ssh_configdebug1: /etc/ssh/ssh_config line 21: include /etc/ssh/ssh_config.d/* matched no filesdebug1: /etc/ssh/ssh_config line 54: Applying options for *debug1: Authenticator provider $SSH_SK_PROVIDER did not resolve; disablingdebug1: Executing proxy command: exec ssh -W other_host:22 hostdebug1: identity file /Users/my_username/.ssh/id_rsa type 0debug1: identity file /Users/my_username/.ssh/id_rsa-cert type -1debug1: identity file /Users/my_username/.ssh/id_ecdsa type -1debug1: identity file /Users/my_username/.ssh/id_ecdsa-cert type -1debug1: identity file /Users/my_username/.ssh/id_ecdsa_sk type -1debug1: identity file /Users/my_username/.ssh/id_ecdsa_sk-cert type -1debug1: identity file /Users/my_username/.ssh/id_ed25519 type 3debug1: identity file /Users/my_username/.ssh/id_ed25519-cert type -1debug1: identity file /Users/my_username/.ssh/id_ed25519_sk type -1debug1: identity file /Users/my_username/.ssh/id_ed25519_sk-cert type -1debug1: identity file /Users/my_username/.ssh/id_xmss type -1debug1: identity file /Users/my_username/.ssh/id_xmss-cert type -1debug1: identity file /Users/my_username/.ssh/id_dsa type -1debug1: identity file /Users/my_username/.ssh/id_dsa-cert type -1debug1: Local version string SSH-2.0-OpenSSH_9.8username@host.it's password:

The SSH config is the following (I'm running other_host but it's the ProxyCommand that is asking for the password, the connection from host to other_host works fine all the times):

Host host  HostName host.it  Port 22  User user  IdentityFile ~/.ssh/id_ed25519  ServerAliveInterval 60  ServerAliveCountMax 3  TCPKeepAlive yesHost other_host  HostName other_host  Port 22  User user  ProxyCommand ssh -W %h:%p host  ServerAliveInterval 60  ServerAliveCountMax 3  TCPKeepAlive yes

Update:
seems like the server i usin kerberos with session tickets, so probably the home folder is no accessible when logging in. So I though to add a krenew -b -K 604800 in .bashrc, however I get:

$ krenew -b -K 604800krenew: error reading ticket cache: No credentials cache found (filename: /tmp/krb5cc_15521)