Welp, that's really an extreme edge case.
Is your browser made from scratch ? Or is it a fork of WebKit ? Because if it's a fork of a known browser it could be just as easy as adding the bundle identifier. streamdetection uses AppleScript to talk with the browsers (ScriptingBridge).
Else, I'd suggest you make your own streamdetection binary (and then replace the file). Here's the basic code to make it communicate with HAPU: https://gist.github.com/inket/531f64812950036b4345
Just change the lines 22-27 to read the anime information from your browser. For Crunchyroll it's a pretty straightforward regex to extract the information from the window/tab title.