Upgrades to a major version add new modules and delete other modules,  usually this mean transforming the data in your database, this is done with scripts, both odoo and the community develop such scripts, after you database has been upgraded, and since with docker the database lives in a different container, you would just start a container with the newer version of odoo and attach the database container to it. Your modules should be mounted to the odoo container and if you followed odoo conventions, your module shouldn't be broken, or it just may need minor modifications to cope with the changes in the newer version.

Upgrading to a minor version should be as easy as using another version of the odoo container, you stop the old one and start the new one and as usual, attach the db container to the odoo container.