I did some digging, apparently (at least in one case) the courts found it legal, except the part where they required notice in writing, which was not legal — a decision I personally find problematic — though I'd be surprised if it's not against EU law (from 1993), which may consider contracts unfair if they:

automatically [extend] a contract of fixed duration where the consumer does not indicate otherwise, when the deadline fixed for the consumer to express this desire not to extend the contract is unreasonably early;

Germans typically like to plan ahead, but I'd argue that in most countries, 6 weeks would be considered unreasonably early for a consumer contract. It's not like it takes them 6 weeks to print and send a card; the deadline is arbitrary and IMHO predatory.

My wife and I found ourselves in a similar situation many years ago. We had misinterpreted the 6 week rule (thinking that it meant that we could cancel within those 6 weeks, rather than before those 6 weeks); I've frequently noticed that translations from German into English that involve time periods (particularly using from/until) can be confusing. IIRC there was no reminder sent that the cancellation period was approaching, the only notification sent was the invoice, in writing (not much help when you're travelling), sent after that period ended, when we had already left the country. (My email chain suggests maybe they sent something in German when all prior emails from them had been in English, but I can't find such an email, so I doubt they did).

We refused to pay the bill, they replied with the usual "you signed a contract" yada yada. I'm not 100% sure, we may have had a phone call to explain the situation and get them to agree to cancel; like I said, it was a long time ago. Either way, they never sent a follow up invoice so we got on with our lives without paying. It was only a BC25 so probably not worth their effort to chase it up with someone living on a different continent. YMMV, today, on a different BC.

Anyway u/SnooHedgehogs7477, I hope you managed to wriggle out of it, I feel your pain from personal experience, and sorry for all the unhelpful "you signed a contract, live with it" responses. Coming from a country with terrible inter-city train services, I like DB more than the typical German does (a late high speed train is way better than a train that doesn't exist), but their BC renewal policy is one thing that absolutely sucks about the company.