If I understand correctly.
You want to update from 3.2.2 to 3.2.9.
The procedure to follow = https://www.phpbb.com/support/documents ... pdate_full
This is using the full package, but using the changed files packages is just as trustworthy
There are a couple of caveats though.
For one: from your printscreen it seems an autoupdate or patching was used which means your starting files may have been changed already and since there were problems, only the full package should be used to ensure that all previous errors are removed.
I'm assuming that you have a full files and database backup so that you still have 3.2.1 (or 3.2.2) in full working order.
Take into account that any file edits you made previously will have to be redone (and may not work on the new version of phpBB. In cases like this, it always a good idea to test an update (and modifications) on a personal webserver before doing a live update/grade
Second: since you're having a timeout problem: truncate the search tables - these can be refilled after updating
Third: before starting the update, eliminate all possible sources of problems: e.g. outdated extensions. This also includes language packs and styles.
Disable or uninstall anything you don't need before updating and check for updated versions.
And (as mentioned before): in /store remove any migrationsXXX, io_lock.lock and install_config.php before starting the update, and purge the cache before starting the update.
Looking at the size of your board - that shouldn't be a problem for updating (nor upgrading) at all and CLI shouldn't be necessary.
If you continue to have problems, I'm willing to have a look at your board and update it myself (on localhost) and then send it back to you. that would be Wednesday evening or Thursday at the earliest. You can PM me if necessary (oh, and no payment involved).