I reported this as it means to me that the cat found a big hole in the chair and went inside the chair, it should read 'onto', which can mean the seat, the arms or the back of the chair where cats usually like to sit
The Hungarian sentence could mean both I think. But unusual anyway.
With the arms and back surrounding it - you could say "into".
Do Hungarians say crawl into? English speakers would say crawl onto.
No, Hungarians say "bemászik" or "felmászik". But every cat and every armchair is different.