[DEPR] Assorted footguns in dtype checks

[jbrockmendel]

Finding some things that don't behave in The Obvious Way:

• dtypes.common.is_period
  Never used outside of tests, checks for PeriodDtype-like arrays, not Period scalar.
• dtypes.common.is_datetimelike
  Checks for datetime64_dtype, datetime64tz_dtype, PeriodIndex, or timedelta64_dtype, the last of which is not obvious (and in fact caused some bugs that will be fixed by [Bug] Fix various DatetimeIndex comparison bugs #22074)
• dtypes.common.is_int_or_datetime_dtype only used in two places, better to write out the conditions explicitly.
• dtypes.common.is_floating_dtype deprecated in 0.20.0, is it too early to remove?
• dtypes.common.is_datetimetz appears to be a duplicate of is_datetime64tz_dtype
• lib.is_integer
  Returns True for timedelta64 objects; inconsistent with is_integer_dtype which excludes timedelta64.

[gfyoung]

xref #16242