It is really getting rarer, also there are plenty of ways to easily circumvent it these days. I remember back in the 90s we just went to the Netherlands and got Mortal Kombat 2 and anything our teenage heart desired. These days you don't even have to leave the room to "go to the netherlands". Also cut versions of games because of violence are a rare occurence these days. The last two games that were put on the index were Dying Light(which is the most retarded decision ever especially comparing it to other games that were not put on the index), and Hatred. Really the only consequence of this is that you can't buy them on the german steam store(which could theoretically still sell them if valve had some form of age verification). You can still obtain them with ease from other stores.

Stuff like Fallout NV which had a low violence version on release in germany as the only option is now available uncut in the GOTY edition or whatever it is called.

So it used to be really bad(and the agency responsible still does retarded shit), it's not more than an annoyance(I'd say not even that), especially if you are over 18(which I would guess you are if you would like to relocate to germany from wherever you may be). Living in Berlin as an adult you would probably not even notice anything the BPjM does(if you are not into national socialism and nazi hatespeech and stuff like that, but even that dreck is not hard to find if you know where to look).

The BPjM(the guys who get to decide what to ban) is fighting a losing battle ever since it's inception, and with the endless possibilities of the internet nothing they do really has any tangible impact. I just read their report from last year and it's mostly comprised of obscure torture porn, german gangster rap youtube videos(wtf) and nazi publications and music, all of which is easily accessible to anyone who can navigate the internet.