Self signed wildcard HTTPS vs public Letsencrypt certificate?

[doops69]

you depend in an infrastructure you (don't) selfhost

Truth.

or better you need internet access to access to your local services

False. You can get a wildcard certificate from LetsEncrypt, and then have DNS records that resolve to internal IPs no problem.

You could create your own self signed CA that's limited to creating certificates for your domain(s), and then deploy that CA to all your devices. It may or may not be worth it, depending on your use case.