To clarify, the $12 / year would be the cost of the domain name, running the stack should be close to free.
For small websites you can often find ways to fit inside free tiers these days. If this site is just static files you could use similarly use netlify (100GB/month free). Or you could use a free tier VPS from GCP/AWS and cloudflare to cache traffic (to keep you under the free tier bandwidth limits). Or so on.