smpl
Your fellow competitors did not necessarily perform the search when they were at the pub. It could be a the john when they got home. Your data profile is still tied to them right now.
Have you looked at the OpenSearch Description file for your instance? It might be generated with an IP by SearXNG not knowing the hostname. The URL is probably https://search.home/opensearch.xml.
If you want to examine the search engines in your browser profile, they're stored in a json file compressed with a mozilla specific variant of lz4. The file is search.json.mozlz4 and can be unpacked to json with lz4json.
I'd recommend you donate money to those who host open infrastructure. That stuff is expensive and critical to the free and open internet.
As for free software projects I suggest donating your time with contributions. That's what they need the most. Helping with bug reports and writing documentation are easy starters and worth much more than money. That's hard to sell as a gift though.. One gift card for confirming and investigating a bug in free software of choice. Merry Christmas Uncle Bob!
Going from being a cool hacker who does things for fun and share it with his peers to being a poor cyberbeggar does no good to a persons selfworth. Help out by contributing and let Mr. Cool Hacker have time for his day job on the side. We get better software and fewer burnouts.
First thing I would ask the ISP to open the port. I've done that without problems before.
If that's for some reason not a solution, I would, because I'm personally not very attracted to the idea of routing my selfhosting traffic though thirdparties, setup a simple static page with <meta http-equiv="refresh" content="0;url=https://web.domain.tld:8080/" />, somewhere and point the bare domain and www subdomain to that page and have it redirect to, like in this example, a web subdomain with the port number.
As a last remark, I personally would not find it problematic for a different port number to be part of the host scheme and also note that most web traffic now goes to 443 and not 80 because it's https.
Happy selfhosting!