I've accidentally found out that it's possible to view the list of my Strava support tickets in the mobile app. However, it's quite cumbersome to find them (need to open any Help text and then, seemingly randomly, there is or is not a “pen” icon in top right, which would open the list of my tickets & updates.)
This really should be accessible easier (and more reliably too - the current path mentioned above works quite unpredictably), i.e. directly from the app menu - perhaps it would make most sense to include in Settings > Help; and it would also be helpful if we could enable push notifications for ticket updates.
