Login to the MogStation, select Steam Payment from the landing page, select Entry or Standard and then 30 days, select Steam Wallet then once it asks you to login to the Steam website simply click "Add Funds" if the Wallet doesn't have enough, charge it, done.

You can add funds from multiple sources, none of which have anything to do with SE.

Unsure if selecting Auto-Renew requires some form of check, but it should not.

How are you getting an invalid address error with the Steam version, where in that process I mentioned above?