[inquisitor]

That looks good (in the sense that there's no active tariff option), except for your balance on the customer portal which obviously lags behind. You should wait a couple of hours and retry ordering through the app or their website and if both fails your only option left is ordering your bundle through the voice-guided menu available at 1155, however I'm not sure if calls to this number are being charged when calling from the US. So better wait until you step on German soil before you burn your credit quickly. Depending on how well your German is, you may also find it difficult to cope with the spoken instructions. I was able to find a two years old forum post where someone described the key sequence for ordering the 5GB data pack:
call 1155, press "8", "1", "1", "2"
However I'm note sure if that is still valid as the tariff portofolio has seen changes since then.