Have a look at https://forwardemail.net/. It’s a service that handles accepting (and optionally sending) email on your domain, and forwarding any received mail to other backend services, like a gmail account. All you need to do is set some DNS records, like MX and their servers will handle everything. It works fine with domains hosted on cloudflare, and has excellent howto’s to get everything set up and running.
Edit: The great thing about this service, imho, is their guides. They don’t just have a static howto, they template in your information into the exact string you need to copy/paste into the service provider’s web interface. Want to encrypt your plaintext TXT records? There’s a button for that on the guide. Want to learn how to get around a port 25 ISP block, they have a guide for that. Want to set up proper Send-As from Gmail using their SMTP server? There’s a guide for that. :-)
Proxmox is Debian. :-)
I do always suggest installing Debian first, and then installing Proxmox on top. This allows you to properly set up your disks, and networking as needed, as the Proxmox installer is a bit limited: https://pve.proxmox.com/wiki/Install_Proxmox_VE_on_Debian_12_Bookworm
Once you have it up and running, have a look at the CT Templates. There’s a whole set of pre-configured templates from TurnkeyLinux (again, debian+) that make it trivial to set up all kinds of services in lightweight LXC Containers.
For Home Assistant a VM is your best bet, as it makes setting up connectivity way easier than messing with docker networking. It also allows easy USB passthrough, for things like ZWave/Zigbee/Bluetooth adapters.