[reland][libc][NFC] Implement `FPBits` in terms of `FloatProperties` to reduce...

[reland][libc][NFC] Implement `FPBits` in terms of `FloatProperties` to reduce clutter (#75196) (#75318)

Also make type naming consistent by using `UIntType` instead of
`intU_t`.
This patch is a reland of #75196 but does not include the "use `FPBits`
instead of `FPBits_t`, `FPB`" part. This needs more work.