Certificate chain of trust: I assume you’re talking about PKI infrastructure and using root CAs + Derivative CAs? If yes, then I must note that I’m not planning to run derivative CAs because it’s just for my lab and I don’t need that much of infrastructure.

An intermediate CA could potentially be useful, but isn't really needed in self-signed CA. But in case you have to revoke your rootCA, you have to replace that certificate on all your devices, which can become a lot of hassle if you share that trusted root CA with family/friends. By having a intermediate CA and hiding your root CAs private key somewhere offline, you could take away that overheat by just revoking the intermediate CA and updating the server certificate with the newly signed Intermediate bundle and serving that new certificate through the proxy. (Hope that makes sense? :|)

I do not know what X.509 extensions are and why I need them. Could you tell me more?

This will probably give you some better explanation than I could :| I have everything written in a markdown file, and reading through my notes I remember I had to put some basic constraints TRUE in my certificates to make them work on my android root store ! Some are necessary to make your root CA work properly (like CA:True). Also if you want SAN certificates (multidomaine) you have to put them in your x509 extensions.

’m also considering client certificates as an alternative to SSO, am I right in considering them this way?

Ohhh, I don't know... I haven't installed or used any SSO service and thinking of MFA/SSO with authelia in the future ! My guess would be that those are 2 different technologies and could work together? Having self-signed CA with a 2FA could possible work in a homelab but I have no idea how because I haven't tested it out. But thinks to consider if you want clients certificates for your family/friends is to have a intermediate CA in case of revocation, you don't have to replace the certificate in their root store every time you sign a new Intermediate CA.

I’ll mention that I plan to run an instance of HAProxy per podman pod so that I terminate my encrypted traffic inside the pod and exclusively route unencrypted traffic through local host inside the pod.

I have no idea about HAProxy and podman and how they work to encrypt traffic. All my traffic passes through a wireguard tunnel to my docker containers/proxy which I consider safe enough? Listening to all my traffic with wireshark seamed to do exactly what I'm expecting but I'm not an expert :L So I cannot help you further on that topic. But I will keep your idea in my notes to see If there could be further improvement in my setup with HAProxy and podman compared to docker and traefik through wireguard tunnel.

Of course, that means that every pod on my network (hosting an HAProxy instance) will be given a distinct subdomain, and I will be producing certificates for specific subdomains, instead of using a wildcard.

Openssl SAN certificates are going to be a life/time saver in your setup ! One certificat with multidomian !

I'm just a hobby homelaber/tinkerer so take everything with caution and always double check with other sources ! :) Hope it helps !

Edit

Thinking of your use case I would personally create a rootCA and an intermediateCA + certificate bundle. Put the rootCA in the trusted store on all your devices and serve the intermediateCA/certificate bundle with your proxy of choice. Signing the certificate with SAN X.509 extension for all your domains. Save your rootCA's key somwhere offline to keep it save !

The links I gave you are very useful but every bit of information is a bit dispatched and you have to combine them by yourself, but it's a gold mine of information !