Theres no way to integrate into the built in settings module. You can create your own settings module and add a button to your module to access it.
You can only access options exposed explicitly in the API. Theres no generic way to access them.
You can also store settings for your digitalmod so StreetDeck saves them automatically for you in a HORM compatible way on shutdown and sleep by using the module and overlay functions of GetStringOption / SetStringOption. There are also similar functions for integers and booleans. Each category for each module / overlay has a maximum of 25 options.