Replace `cache_in_self` with `functools.cached_property`

This issue has been migrated from [#11545](https://github.com/matrix-org/synapse/issues/11545).

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This acts a loss less magic-y and more pythonic by storing the result of its value as a direct name mapping in the instance itself.

In other words, this'll make the property function run once, and then store its value as the same name of the property, which can then be read and written to like any normal value.

To me, this looks a loss less hack-y than `cache_in_self`, which currently does it with underscore-prefixed values.

However, this is only available to synapse once 3.8 is the lowest supported python, see the [docs](https://docs.python.org/3/library/functools.html#functools.cached_property)