True identity key rotation seems somewhat important in the long term

This only shows that in Matrix group metadata, membership and permissions is not E2E protected. It is instead protected with homeserver keys. IIRC even the group description is not protected for encrypted groups.

In Signal there is something in-between: if you resetup but use Secure Value Recovery (enter a PIN), you get the same account ID (similar to the same email address) and restore your group membership and verifications, but your identity key is changed. Group membership is managed on the server, but in a way that the server cannot see account IDs stored there: Signal >> Blog >> Technology Preview: Signal Private Group System, The Signal Private Group System and Anonymous Credentials Supporting Efficient Verifiable Encryption
What happens if the identity key is actually compromised and available to the attacker is hard to tell, Signal >> Specifications >> The Sesame Algorithm: Session Management for Asynchronous Message Encryption just says “Security is catastrophically compromised if an attacker learns a device’s secret values, such as the identity private key and session state.”

There are Continuous Group Key Agreement protocols in development that can have “post-compromise security” and “clone detection”, but no messenger has deployed it yet AFAIK and the protocols that are being deployed now are not decentralized:

In Delta Chat group membership is managed entirely on devices without any servers, so there is no place where you can recover your group membership from.

If user lost the identity key, the only way to recover from this cryptographically is to tell as many peers as possible that the key is revoked so it is removed from all chats and no messages are sent to encryption keys signed by this identity. Then you need to create a new identity and join the chats with it.

There is a draft for OpenPGP key replacement at draft-ietf-openpgp-replacementkey-03 - OpenPGP Key Replacement but in case of key compromise it cannot work automatically because the key in this case is “hard-revoked”.

For non-cryptographic means see: