tests: net: lib: http_server: core: Cleanup before adding more tests

Do some cleanup regarding naming used in the test suite to prepare it
for adding more test cases.

Extract common setup/teardown into respective before and after ztest
functions to simplify test code. Proper before and after functions also
ensure that individual test case failure does not disrupt other tests
operation.

Split the tests into two separate test suites, one for those which
require pre-setup and second for those which don't.

Finally, enable receive timeout on the client socket to ensure tests
won't stall in case of errors.

Signed-off-by: Robert Lubos <robert.lubos@nordicsemi.no>