Could I set up WireGuard between the home server and VPS then have that handle sending out the email?

Yes, you can.

What software stack would I need? Would this be something like postfix to postfix or..?

I don't think you need postfix-to-postfix. You just configure your VPS server's VPN-facing IP address in your dovecot or mail client (instead of the conventual localhost address).

> Could I set up WireGuard between the home server and VPS then have that handle sending out the email?

Yes, however wireguard protocol is easy to detect, my provider is blocking this protocol, so I use xray (which is not VPN, but can be used as bridge), it works great.

> What software stack would I need? Would this be something like postfix to postfix or..?

As an option: try maddy, it is easy to setup.

Here is a guide that I found helpful when setting up my email server: https://workaround.org/ispmail-bookworm/whats-new/

It allows for multiple aliases and domains. Has spam blocking and uses both postfix and dovecot for handling the mail.

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Vultr blocks outgoing port 25 so you'll have to ask support for it to be opened.

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Test your residential IP by connecting to smtp/imap servers using telnet.

Mailu or mail cow and smtp2go for outgoing. Don’t make a hard decision be harder than it needs to!