Which function should be used to either mask out the unwanted letters and
leave the numbers or extract to another (set of) cells by filtering by
position within the source cell or by the character type desired?

If the numbers are consecutive:

=LOOKUP(9.99999999999999E+307,--MID(A1,MIN(
SEARCH({0,1,2,3,4,5,6,7,8,9},A1& "0123456789")),
ROW(INDIRECT("1:"&LEN(A1)))))

Here is a non-volatile formula which will do the same thing...

=--MID(A1,MIN(FIND({0,1,2,3,4,5,6,7,8,9},A1&"01234567 89")),SUMPRODUCT(--ISNUMBER(--MID(A1,ROW($1:$999),1))))

Rick