For some reasons, I had to reinstall nextcloud (as docker image).
What I now lost are my old tasks, but I have a backup of the old installation volume.
Where are the tasks (Tasks app) stored? The installation used sqlite. I hoped to find the sqlite files but had no success so far…
You are on the right track, tasks should be stored in the SQLite database, which you should find in the Nextcloud data directory by default (data/ from the Nextcloud document root or e.g. /var/www/nextcloud/data). The database file should be named nextcloud.db.
The name of the SQLite database is actually owncloud.db. You should find it in Nextclouds data-folder as @j-ed wrote.
Once you found the database you could easily export the tasks with the script calcardbackup. Have a look the section „does this also work with a broken instance“ in the README of the repository for how to accomplish this.