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I mean your hosting – are you running the server will full root access? Is it shared hosting? Somewhere in between?

If you run the server, it's easy-peasy to put-in a VirtualHost directive in your Apache configs that'll map mydomain.tld to otherdomain.tld serving from the same root directory

Once you've done that, and you have all your SSL certs in place for the new domain, update your blog's settings to use the new domain

And everything should have migrated "seamlessly"