DEPR: move NumericIndex._engine_type and .inferred_type to Index

[topper-123]

Moves_engine_type & inferred_type from NumericIndexto Index in preparation to remove NumericIndex and include numpy int/uint/float64 in the base Index.

xref #42717.

[jbrockmendel]

needs rebase

[topper-123]

Ping.

[jbrockmendel]

this doesnt change anything for our nullable dtypes, but in principle could be an API change for 3rd party EAs. worth caring about @mroeschke ?

[mroeschke]

I think this would be a good API change for ArrowDtype, but not sure what else subsequently relies on the output of Index.inferred_type

[topper-123]

This change I proposed isn't strictly needed, I just added it as an optimization. I could also remove it here and try do add something similar to lib.infer_dtype instead. It's also a better location for this IMO and at least we can discuss if there's some down side to doing this seperately from the NumericIndex removal process.

[jbrockmendel]

to avoid the api change you can do:

if isinstance(self.dtype, np.dtype) and self.dtype.kind in "iufc":
    [...]
return lib.infer_dtype(...)

[topper-123]

Ok, I can do it like that.

[topper-123]

Updated.

[mroeschke]

Thanks @topper-123