Hi!

A booked option has a term of 28 days. You couldn't use it at all?

Hey!

No. From the SMS it says I have the tariff active until the 28.02.2020 but the app or website, both say I have no data available, and it is not as if I have used everything, it says that there is no actual data, as I have never bought anything.

Ok, then you didn't mean January 1st, but February 1st. ;)
What is the status of the option? Active, inactive, waiting to be charged? https://www.o2online.de/ecare-prepaid/tarifdetails

If you look in Mein o2, you will see the sentence “Übersicht der letzen 6 Monate” (Overview of the last 6 months) in the middle of the following page: https://www.o2online.de/ecare-prepaid/uebersicht
Click once on the link and a window will open.
Check that the package is listed there and that there is a start and an end date.
If the start and end dates are identical, the package was not activated but deactivated.
Many users make the following mistake: They book an option and use it. Almost all options are automatically extended if the credit is sufficient. If you don´t have enough credit, the option is paused and if the credit should be sufficient after topping up, the option is automatically activated again. And here the users think that they have to reactivate the option and thereby cancel the option.

An o2 employee will review your question in the coming days. Perhaps it is possible that the credit will be refunded or the option reactivated.

Yes, you are right, I made a mistake, I topped up on the 01.02.2020.

The status says aktiv for “Datenautomatik Loop”.

Yes,  this is what I see in the overview: 

As you mentioned, the package was thus deactivated.

Is it possible that I can reactivate it myself?

Thank you for the answer!

Ok, the "well known user mistake" ;)
You cannot reactivate it yourself.
Unfortunately, you have to wait for further help if the hotline “doesn't want to understand you”.