test-parse-util: Move parse-util tests into their own test case

test-parse-util: Move parse-util tests into their own test case

Tests for the functions defined in src/basic/parse-util.c. Reorder them
to match the order in which the functions are defined in the source
file. Adjusted the list of include files to remove the ones no longer
needed in test-util.c.

Tested that `make check` still passes as expected. Also checked the
number of lines removed from test-util.c matches the expected, as an
additional verification that no tests were dropped or duplicated in the
move.