I do that with Termux on my Android phone. I set up dynamic DNS and wireguard on my router so I can reach my LAN from anywhere. I just enable wireguard and ssh in.
Not sure if there's a Termux equivalent for iPhone.
Free, OSS, pretty great for ssh via VPN => tmux a => codex/claude
I set up Codex to send a notification when done over Pushover (https://pushover.net). With this setup, you can just ssh into a Mac or Linux box either way.
Not sure if there's a Termux equivalent for iPhone.