I've merged both issues onto the same thread, since they're discussing the same problem. (Do you have two accounts? The screenshots posted look identical. If so, there's usually no reason to post a topic twice, it just makes it harder for us to keep track of and answer all questions.)
The error is raised by
peewee, which Prodigy uses to manage database connections, and it indicates that for some reason, your MySQL connection timed out. Maybe you need to increase the connection timout limit in your container.
In any case, try connecting to your database with
peewee directly, in a small script etc. and test a few opterations. This lets you isolate the database connection and makes it easier to debug. If you can connect with
peewee and write to and read from your database, it should work fine in Prodigy. You can also use the
test_database.py test script from here to check your connection from Prodigy.