One time key counts differ between /sync and /keys/upload

This issue has been migrated from [#10766](https://github.com/matrix-org/synapse/issues/10766).

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### Description

I noticed that after sending an encrypted in a large E2EE room ([#e2ee-test:grin.hu](https://matrix.to/#/%23e2ee-test%3Agrin.hu)) my key count responses got out of sync (might have happened earlier). On sync I got a count of 55, while when doing an empty key upload request returned a count of 33. Does synapse cache the key count for /sync somehow and that got out of sync?

After uploading some keys, the counts synchronized themselves to 50, so I am assuming the ones in /sync were wrong.

### Steps to reproduce

- after sending some e2ee messages, check what an empty key upload response returns vs the count in /sync.

### Version information

- **Homeserver**: neko.dev

If not matrix.org:

- **Version**: 1.42.0rc1

- **Install method**: ebuild

- **Platform**: Gentoo