Open balcony door for the cat to have access the balcony

I have a small project here and would love some input to figure out the best way to make it work.

There’s a door in my kitchen that leads to a semi-enclosed balcony. On that balcony, I keep my cat’s Petkit litter box, Petkit food bowl, and PetKit water dispenser. However, since the balcony is partially open, leaving the door ajar during winter makes the house unbearably cold. So I had the idea of installing a motor to automate the door. I purchased a Tuya 24V automatic window opener with a sliding arm, designed to open casement windows up to 90 degrees, and plan to connect it to a Shelly Wave Shutter to control the door’s opening and closing.

The door has a latch, so to ensure it opens and closes properly, I’m also planning to install a smart lock. I’ve got a Yale Linus sitting around, waiting to be used…

The Challenge

I want the door to open when my cat approaches (it opens outward, so it won’t swing toward her) and to close once she returns from the balcony. I won’t close the door while she’s still out there, since it opens outward and could hit her — even though cats are pretty agile.

I’m trying to figure out how to detect when she’s near the door and when she’s come back inside. I could use a motion or presence sensor, but I’d probably need two (one inside and one outside) to detect direction. I also don’t want the door to open every time someone’s just in the kitchen and not intending to go out.

For humans, I’ll set up an automation: when the Yale lock is unlocked, the motor activates and the door stays open. I might also add a Zigbee button and a sensor to monitor the door’s status.

In Summary

Does anyone have ideas for creating an automation specifically for the cat? I considered a collar with an NFC or RFID chip, but that would require her to physically touch something, which isn’t practical.

Bluetooth sensor condtion:min RSSI
Motion, beam or preferably mmw sensor for proximity.

Open door when Bluetooth sensed @ XX RSSI and the proximity sensor is tripped.

EDIT
Pressure mat may be added also.

Camera with object(cat) detection

All of these I feel will false alarm when cat gets close but not want in/ out