The Contribute menu (T322740) is available in a small set of pilot wikis. Once key improvements based on their feedback such as T369041 are completed, we can consider expanding the enablements. As a next step we can consider to enable the Contribute menu on mobile for wikis where section translation is enabled.
In this way, a main entry point can be provided to the mobile translation dashboard, and the exposure can still be limited by targetting only the mobile platform for now.
I've moved tasks relating to the contribute entry point to the language team backlog as the language team are still working on this and web is not. @Pginer-WMF feel free to re-tag web team if you need to request code review from us!
@KartikMistry after enabling the contribute entry point to wikis where section translation is enabled, would it be possible for this to happen automatically for new Wikipedias created in the future? Or, if not fully automatic, maybe considered as part of the semi-automated process described in T371420?