Extend "Macintosh HD" volume with a new, additional disk - ?

No easy way to do it, and even if done I consider it too risky to be worthwhile. Macintosh HD is a very complex beast that warrants extreme care. IMHO you should do nothing with Macintosh HD other than install apps and/or perhaps create additional volumes if needed, but that does not increase the available space.

Keep your external drive separate and manage your data accordingly. You do know that you can move most data off the internal drive and continue to operate just fine? For example, I keep my entire photo, music, video & TV libraries as well as Documents & Downloads on an external drive and have never seen any difference in performance vs. having the data on the internal drive.

You cannot do that. Just use the external to hold large files like Photos, Music, Movies, etc.. The alt. is to use a larger external as a clone boot drive but then AI will not be available.