Welcome to the forum! This feature is already available in both the Now Playing and Track Information Panels:
Preferences/Internet/custom web links
You can add your own entries. For example, to add a Google search for the tagged artist name plus the word "band", you might enter "Google band" as a name, and the web link as: https://www.google.com/search?&q=<Artist> band
Vary the tag name in <> and any extra search terms or tags to your taste. As the preferences indicate, right-click in the panel to see the built-in and custom links. Other sites can be added the same way, such as:
Soundcloud https://soundcloud.com/search?&q=<Artist> <Title>
And check out redwing's cool album cover search string here:
https://getmusicbee.com/forum/index.php?topic=24540.0