ENH: implement Float16Engine

[jbrockmendel]

cc @topper-123

If we do go down this path, I'll try to fix the xfails before merging.

[phofl]

Do we want to add this generally? Float16 works more or less nowhere

[jbrockmendel]

context is #49536, this is largely a proof of concept

[topper-123]

I don't have a string opinion on 16bit floats, they're probably very rarely used, that most users won't use them, thought from a API completeness perspective, they're good to have. So I'm probably +0 on adding float16 indexes.

IF it is decided to go through with this, float16 should be added to pandas/tests/indexes/numeric/test_numeric.py::TestFloatNumericIndex::dtype and probably in other places.

[jbrockmendel]

I'm pretty happy to defer to @topper-123 on this topic. should we close this?

[topper-123]

I would very much would like #49536 to get merged, i.e. so I'm in favor of closing this for now, or at least not having #49536 dependant on this PR. If someone wants float16 indexes, it can always be opened a new PR later (though I'm a bit apprehensive about if because of the lack of float16_t in numpy).

I'll close this PR for now.