When your domain is close to running out, you should either get an email from your registrar asking you to renew, or a payment notification telling you that your domain will be renewed for whatever price automatically.

If the payment fails, the domain will be temporarily suspended. There is a grace period where nobody can buy that domain, allowing you to settle the missed payment. If you do not settle the payment, the domain will be put back up for sale

None of this affects whatever services you’re running on your Pi, people just won’t be able to connect to it if your domain is suspended.

I’d suggest looking into SSL certificates (Letsencrypt is free) as well as Cloudflare for masking your Pi (your home) IP address from users of your instance - do note this has privacy implications: cloudflare becomes a MITM for your site

Freenom is being sued by Meta (Facebook) at the moment for supposedly not dealing with spam domains. I would not recommend using a Freenom domain if/when they reopen registrations: FMHY had their old Freenom lemmy instance domain seized by Mali’s government