Your data is not lost. If you don't have any backup of the files, you can still do a fresh install and import your database and avatar files. You'll have to re-install every extension but no data will be lost.
Alternatively you can copy the entire broken forum to a different server or local computer with SSH and Composer, and run Composer update manually.
Maybe someone more familiar with the extension manager can chime in. I believe the manager creates a second vendor folder during the upgrade. If the process failed before it finished, you might still have the old vendor folder on your system and can manually rename it.
Shared hosting is perfectly fine, but we still recommend choosing one with SSH access as it will give the greatest flexibility.
For users with no SSH, I'm sure we can still improve things. It's inherently dangerous to update the software from within the software itself. The more reliable solution would be to have a graphical Composer solution as a separate app on the webserver, so if anything breaks you can still re-run the failed command. The extension manager should probably have additional logic to verify all Composer files were properly generated before switching from old to new vendor folder.
I am curious what happened in your case, because I have only ever seen that error with people who used Composer over the command line. It would be interesting to figure out what happened so we can ensure the extension manager is resilient to this is the future.
Can you give us more information on the hosting ? Company, PHP version? Have you configured the scheduler or asynchronous queues ?
