Yes it is illegal. Though it does not warrant the use of force.

Section 185 Insult: The penalty for insult is imprisonment for a term not exceeding one year or a fine and, if the insult is committed publicly, in a meeting, by disseminating content (section 11 (3)) or by means of an assault, imprisonment for a term not exceeding two years or a fine.

While I personally am unsure about the handling of that situation, I think police is legally able to justify the use of force in this situation by saying "Oh, the situation was difficult and we had to act now to ensure that we are able to identify the person." The woman who tried to "help" the man by intervening is legally also in trouble; if the police had the capacity and the will to act.

Funfact: Generally, you can call them "cows" in German so "Bulle", because it is so well established that it no longer counts as an insult but only as colloquial language.

the europeans seem to be going harder on fascism than the americans atm.

I disagree with what you are implying in the second sentence, but agree with the third. I don't believe that in general (so individuals might) the police acts more forceful against pro-Palestine demonstrators. However, I do agree that politically Germany is doing fuck all for Palestine.

That's fair. Context is of course always relative. In would say context is given if the starts at the first interaction of the person taken in custody with the police. Of course its difficult to find such high quality footage. Not sure if it is worth to point out but many police officers are in favor of bodycams. They cannot use them because they are against the law in Germany. If I find a video with more context, I will get back to you, but I am pretty bad at that.

That being said: There are definitely police officers out there that love going on demonstrations and smacking people. I personally know one who did this who lost his job as a police officer; not sure whether it was because of that or something else though.