create distinct calendar reservation

Problem/Motivation

I want to create a site for booking workstation or desk in a room.
reservations can be of long duration (many months or even a year) or only a few hours of a day.
reservations are made by a manager for their users, they do not need approval but there cannot be two reservations of the same desk/workstation in the same period.
The previous site created and managed by someone else was in drupal 7 and used MERCI' for managing them.

Steps to reproduce

In drupal 10.2.7 i have installed:
bookable calendar to date reservations
fullcalendar to display them in a calendar

I created a content type defined Reservation with the following fields:
Tutor user reference

Reservation date range

Calendar reference to bookable calendar

Workstation selection list

Proposed resolution

I tried to install and use BAT but I don't understand how it works,
instead intercept I couldn't install it because of compatibility problems with address module.
I have try to update at 10.3 drupal but there are't difference.

Remaining tasks

I am not an experienced user and have difficulty handling code or adding patches.
how can i do it?