How to do operations on cells that contain letters

You don't need a helper column (but even if you did it wouldn't be that big a deal and could even be hidden). You can just use your lookup table:
=AVERAGE(XLOOKUP(A2:A4, Grades[letters], Grades[values], ""))
In this case I used "Format as Table" to make the table of grades and values and named the table "Grades", but you could replace Grdae[letters] with the corresponding range.
If a grade entry doesn't match a value in the table I used "" to ignore it, but you might prefer to remove that so you get an error and you know to look into it to find out why.

Notice how the D is ignored because there is no "D" in the table of Grades to the right

One more note: If you really don't like looking at all that inside the formula and want it to look like the simple AVERAGE(A2:A4) you could create a LAMBDA function (inside your named manager) something like

AVERAGEGRADES =

LAMBDA(grades, AVERAGE(XLOOKUP(grades, Grades[letters], Grades[values], "")))

then you can just enter in you cell:

AVERAGEGRADES(A2:A4)