Contact Sensor/Reed Switch and Switch/Button to control lights in a closet

I am in the process of renovating my utility closet in the kitchen and I’m exploring the possibility of introducing the following improvement:

I’d like to set up a system for the kitchen utility closet where the lights, preferably using LED strips, automatically turn on and remain illuminated for 5 minutes unless the door is closed before the time elapses. Additionally, if we press a button or flip a switch, I want the lights to stay on for 5 minutes unless we press the button/switch again or the door closes. This ensures that we have light in the closet in case the door stays open for longer than 5 minutes and we need light in the closet.

Exploring ideas for the aforementioned solution, would it be possible to do this with a button inline with a reed switch? As I am about to renovate the closet, I am looking to gather suggestions on the optimal approach for implementing the such a solution. If possible, I would like the solution to be fully contained, and be available to for automation, logging and control in Home Assistant.

Thank you in advance.