`Integer`s in the type domain

[nsajko]

Introduce TypeDomainInteger, a subtype of Integer in the type domain. That is, each value is of singleton type.

These type domain integers are then applied to many places in Base (yet other applications are also possible).

To be clear, this should go into Base, as opposed to a user package, because:

• the invalidations when defining a new Integer subtype are horrid
• it should be utilized from within Base, e.g., it fixes the bug below for irrationals

Fixes #37977

Updates #34003

Closes #44538