How to write an automatic shift planner?

Question

Software design

I decided to automate the process of arranging coaches' shifts in the trampoline center because there are a lot of coaches, they have a lot of wishes and it's hard to do it by hand every week. So far, only basic Python is in the arsenal.
A brief description is as follows:
A site where an employee is authorized with a choice of shifts that you can take in a week, then, based on information for all employees, a table is filled in for a week. If interests coincide, randomly fill in the line from the available options.
I was thinking about writing a selection randomization algorithm in Python + JavaScript layout with loading data information from SQL, maybe you can recommend some frameworks for this or simpler tools to complete the task.
To make it clearer, an example UI: