Guarantee vs. guarantee insurance, non-insured parts remain the responsibility of the sale

Evening together, I bought a car and received a guarantee insurance from EinsAuto / GermanAssistance. After half a year the secondary air system is now defective and will cost around 1250€. I think this should not be a problem because the insurance exists. I only thought that, because the damage site shared with me that the secondary air system is not part of the engine but is an attachment part and therefore not covered by the “comprehensive vehicle warranty” w In general, you showed your finger with the tip to be repaired by telephone, since you certainly don’t expect anything, since only parts that are explicitly mentioned in the insurance contract are insured. (The answer to my question was funny, why not call the excluded parts: “No customer would like to read 1000 pages through ” ) So now I stand there with the costs. But this insurance was actually only an addition of the dealer z if the insurance is not responsible, then the warranty obligation would have to fall back on the dealer. Or do you automatically withdraw from all warranty claims if you get such an insurance booklet with it? Does ever have experience with it, because the dealer wants to convince me 100% of this because the warranty insurance is suspended. I hope you can help me. Thanks and Greetings GM