Context and action driven functionality could easily accommodate alternative behavior for each method of invoking Find, Edit>Find|Right Mouse>Find|CTRL-F. To say, "The two (rather three) can't behave differently.", is artificially constraining.
Then again, maybe making a minor adjustment to the current behavior by pre-populating the search value with the currently selected field value, with the value highlighted/selected such that typing any character clears it, while leaving Any field default would suffice... a somewhere in the middle solution.
Currently Find(Find/Replace) only permits searches on a single field. Any reasonable data base system allows logical searches on 1 to N fields. the following example illustrates the simplest form of what should be included in the product:
Find all entries for
Category = XX
Date contains (or ends with) 2020