I have the same experience, (Kaspersky Internet Security on macOSX Monterey),
I have tree computers for different purposes. One of them has macOSX Big Sure and the Kaspersky Internet Security works fine. Now I will not upgrade to Monterey. Other two computers have Monterey and I can not install Kaspersky Internet Security. After several days chats with Kaspersky experts, I did not received any information from them how to solve the problem, finally they told - we sent the problem to experts and i will receive the solution by emaill