* `operator[]` is constexpr
* `operator<<` and `operator+=` are hidden friends

There are two reasons for this:

1) It is highly unlikely that someone has use for this header,
which has no customization points and only provides simplest
possible main, and cannot link the static library which also
provides a default main implementation.
2) It being a header was causing extra complications with
the convenience headers, and our checking script. This would either
require special handling in the checking script, or would break user's
of the main convenience header.

All in all, it is simpler and better in the long term to remove it,
than to fix its problems.

This means that bit-flag-like types with conversion to bool can be
asserted on, like so `REQUIRE(var & Flags::AddNewline)`.

-- Combined with f4fc2dab2c5bb8cab11b0a0dde8a8421076c30f9
   during cherry-picking.

Originally the tests were from #1912, but as it turned out, the issue
was somewhere else. Still, the inputs provided were interesting, so
they are now part of our test suite.