This idea has come up a couple times in the recent past so I figured I would start centralizing it here.
enum.StrEnum is new in Python 3.11, so we'll be able to use it when we drop support for 3.10¹.

There are a handful places in astropy where some exposed parameters only have a few accepted string values. It would make sense to convert user inputs to StrEnum internally to:

1. ensure the value is acceptable (an error is raised otherwise)
2. allow typecheckers to verify exhaustiveness in if/elif/.../else (or match/case/case/...) branches associated with these variables (this is a medium to long term goal, since we don't typecheck yet)

Since I'm using a couple relatively new concepts here that are not yet used in astropy, I don't want to assume everything I just wrote makes perfect sense to all readers, so let me illustrate my points with the following example

from enum import StrEnum, auto
from typing import Literal, assert_never

class OriginMismatch(StrEnum):
    IGNORE = auto()
	WARN = auto()
    ERROR = auto()

def _prepare_unit_sphere_coords(origin_mismatch: Literal["ignore", "warn", "error"]):
    # runtime validation implemented "for free": any unexpected value will raise a `ValueError`
    _origin_mismatch = OriginMismatch(origin_mismatch)

    match _origin_mismatch:
        case OriginMismatch.IGNORE:
            ...
        case OriginMismatch.WARN:
            ...
        case OriginMismatch.ERROR:
            ...
        case _ as unreachable:  # default
			# type checkers can verify that this branch is unreachable
			# so we cannot forget to update this block if an enum member is added or removed
            assert_never(unreachable)

This example is inspired from a real life situation, see #16246

Other than this example, here are other identified places where this pattern would make sense:

• TYP: add type annotations to a couple utility functions in nddata #16546 (comment)
• Add type annotations to stats subpackage #16562 (comment)
• astropy.timeseries's lombscargle's normalization argument could be validated early as an enum

This list is meant to be updated (not necessarily by me) as examples come along.
Let me also ping a couple people who are already involved in this discussion: @eerovaher @nstarman @jeffjennings