Disable authentication inside LAN?

What are you trying to achieve? I could propose alternatives like using a password manager like bitwarden that would autocomplete login info so login is less of a hassle. You can also use SSH to start/stop/list/etc. VMs so you could create a small local UI or shell script to automate the tasks using key based auth so you don't have to input login data.

I also don't think there's any reason for your proxmox web UI to be available outside your local lan or a VPN. Maybe I'm misunderstanding the question.