Asking for methods that exist on builtin float types but not numpy types gives:

>>> set(dir(float)) - set(dir(np.float32))
{'__getformat__',
 '__getnewargs__',
 '__setformat__',
 '__trunc__',
 'as_integer_ratio',
 'fromhex',
 'hex',
 'is_integer'}

Filtering these to the ones that are not CPython implementation details, we have:

• __trunc__(self) -> int, which will enable math.trunc(numpy_float) (ENH: __trunc__ for floating and integer types #28949)
• is_integer(self) -> bool (done in ENH: Add is_integer to np.floating & np.integer  #19803)
• as_integer_ratio(self) -> Tuple[int, int] (done in ENH: Implement np.floating.as_integer_ratio #10741)
• hex(self) -> str (ENH: float.hex and float.fromhex Implementation #20083)
• fromhex(cls: Type[FloatType], s: str) -> FloatType (ENH: float.hex and float.fromhex Implementation #20083)
• from_number(cls:Type[FloatType], number: NumberLike:, /) -> FloatType (ENH: float.from_number implementation #29077)

For all of these, the best approach is probably to port the CPython implementations, taking care to handle the extended precision of long doubles.

Note that we get these methods for free on np.float64 due to inheriting from float