I'd recommend a web proxy service. It acts as a middleman, public > router > port forward to proxy / tailscale > proxy forwards by the domainto the correct service (immich).
Traefic is a good starter one.The most used but more advanced is probably nginx.
For SSL, use https://letsencrypt.org/, there are a bunch of tools to do it and some are automated. They expire faster but are free. Tailscale is a vpn tunnel so the ssl part may not be correct and they may have their own thing though.
Also godaddy is like the worst, expensive, ceo has hunted animals that shouadn't be touched, and I always had outages when dealing with them. Namecheap is good, cloudflare, and porkbun.
You can transfer at any tine and keep the remaining registration time. The only negative is you have to pay the new regristrar a rnewal fee to complete the trasnfer, this adds nore time to your domain, you just would have to pay it early once. They often do deals for transfers especially around holidays.