[jimnotgym]

I think the person above is telling you to set up a webserver to 301 redirect pages from your old domain to your new one. I think that will tell Google that you have chosen to move the site to a new domain, not just copied the site off someone else

[throwaway25239]

The old domain was a *.github.io domain (which I migrated to a custom domain), so I don't think it's possible to use my own server for it.

Google did pick up the relationship correctly, at least in the beginning - the new domain got the same ranking as the old one, and the "backlinks" section of the search console shows links to the old domain under the property information for the new domain. So it seems like this type of redirect does have an effect, unless it somehow expires after a few months and a 301 redirect doesn't?

[montroser]

Yes, this really seems worth a shot, if possible.

If the old site was on a domain that you own, remove the CNAME to github pages, and point it instead to a server you control, that returns 301 redirects to the new site.

The 301's are a standard way to do this, while the meta refresh tags are dubious at best.