I am in Big Sur and in "Music" I cannot seem to be able to do a search of the iTunes Store

JJ 1010,

First, enable the iTunes Store if you don't already have it: Music > Preferences > General, "Show -- iTunes Store." (For unknown reasons, the Store is not enabled by default.)

Then when you search, make sure you're looking in the Store, not in Apple Music, by clicking the iTunes Store icon as pictured below.

jj1010 wrote:

Many thanks! -- the sequence was apparently my issue

You are welcome! :-)