That makes me wonder: What are the rules for something to be considered a browser? Does it need to provide certain functionality, or can I register anything as a browser and just have links open in an editor?
So if you want to make your random executable be "a browser", my guess is you should register it as a handler for http, https, and .html, at least.
Some time ago Microsoft made it impossible to reassign this scheme to another app like EdgeDeflector.
PS: It was KB5007262 that "addresses an issue that might improperly redirect OS functionality when you invoke microsoft-edge: links."