How do I put a cat flap in a panelled door like this?

[Lifebee]

Ideally I'd like to put it in one of the two main panels but they are only 15.5cm wide. The grooved bit between the panels and the sides and centre is thinner and I don't want a draught.
It is an internal door to a utility room which has another cat flap to the garden.
Can you get a cat flap narrow enough to fit in the panels and still allow a regular size cat to get through?

I've seen this before? Not in real life mind, but would this work?

We just have a hole in our internal door and a door curtain. Ours is a solid wood panelled door with glass 🤷🏽‍♀️