I decided to buy a puller because I was tired of pulling the filter out of place with improvised means. I am testing the puller on the example of an Audi a4 b8 Allroad CDNC engine.
For those whose filter sticks badly, there are pullers with a similar operating principle but more powerful on Aliexpress: http://ali.pub/48sj50
just in case, another one: http://ali.pub/48sjmi