Hi, I know this is old post, but it was still on first google page in my lookup for v12->v13 update, so I decided to give a hint for people that couldn’t make Updater going with chown and chmod commands.
I had Nextcloud installation on Fedora server in folder outside of primary Apache folder, so any permission I used, even 777 apache:apache on everything didn’t work, because SELinux was blocking writing. If this is your case, use:
sudo chcon -R -t httpd_sys_rw_content_t /path/to/your/nextcloud/folder