Incorrect notications from intentional mentions which include @room?

This issue has been migrated from [#16460](https://github.com/matrix-org/synapse/issues/16460).

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> Support for intentional mentions was apparently stabilized in https://github.com/matrix-org/synapse/pull/15520 / Synapse v1.86.0rc1, right? Yet, when I just sent a message with `@room` in a code block, which Element Web correctly translated to `m.mentions` being set but without the `room` flag, people *still* got notified.
>
> The [spec](https://spec.matrix.org/latest/client-server-api/#_m_rule_roomnotif) says that the push rule for `@room` should only be enabled if the event does not have an `m.mentions` property.

_Originally posted by @jplatte in https://github.com/matrix-org/synapse/issues/15661#issuecomment-1752915731_