If you have doubts that the increase is lawful, then you can probably have it checked legally as well. An initial consultation usually doesn’t cost much(?) and maybe there are already some findings.
What you then do with the information gained from that is the next question. If the answer is no, they weren’t allowed to do that, then the question is whether blocking 100% really gets you anywhere. At least it would give you a stronger negotiating position, however you then use it (there is a lot of room between swallowing every increase completely and blocking everything).
And if the answer is yes, yes, they were allowed to do that, it would also be important for you to know if they are allowed to do that in the future as well (and if so, to what extent) and what your options are. So, I have no legal knowledge there, but if my bank changes the conditions for my checking account, I can usually cancel with shorter notice periods, etc. Or object, but that can also have consequences. Something like that.
So for me, it would probably be important first of all to know whether what has happened so far was correct and what could actually still come your way. And only someone who knows construction law and dissects your contract again can really explain that to you. (Just because you get advice doesn’t automatically mean you have to sue or anything)