MNT: migrate away from packaging.version.parse

[neutrinoceros]

PR Summary

Currently, packaging.version.parse_version is implemented as

def parse(version):
    # type: (str) -> Union[LegacyVersion, Version]
    """
    Parse the given version string and return either a :class:`Version` object
    or a :class:`LegacyVersion` object depending on if the given version is
    a valid PEP 440 version or a legacy version.
    """
    try:
        return Version(version)
    except InvalidVersion:
        return LegacyVersion(version)

but LegacyVersion is deprecated since pypa/packaging#342

class LegacyVersion(_BaseVersion):
    def __init__(self, version):
        # type: (str) -> None
        self._version = str(version)
        self._key = _legacy_cmpkey(self._version)

        warnings.warn(
            "Creating a LegacyVersion has been deprecated and will be "
            "removed in the next major release",
            DeprecationWarning,
        )

and the plan for their next release is to have packaging.version.parse basically be an alias for packaging.version.Version.__init__, see pypa/packaging#407

So I'm proposing we move forward with it and stop using the parse function as it may cause confusion in the future and is more complicated to use.
Note that since we're now treating warnings as errors in CI (#3380) means that we can switch with confidence because we know that we don't currently have any such warnings to deal with.

[neutrinoceros]

A possible alternative is to build our own parse_version function with a fall back mechanism that would return an object with the same important properties as packaging.version.LegacyVersion, i.e. that would always compare as lower than any given valid version, but I think there's no incentive to do that as long as we don't encounter any issue with the current approach

[neutrinoceros]

@meeseeksdev backport to yt-4.0.x