Just want to check, is there any API to add the authorized domain in a programmatical way instead of adding it manually by going to Firebase console?
Also, is there any limit on how many domains can be added as the authorized domains?
There is no API for this - you must do it through the console. You can also file a feature request with Firebase support if you want.
There doesn't appear to be any documentation stating limits of number of domains. Again, reach out to Firebase support if the documentation is unclear.