Looking at your example workbook (post #1), I'd advice an data entry sheet where all needed data will be entered as table or Defined Table, with columns like:
Date; School; Employee; WhateverYouEnterForWeekdays
and probably additional calculated columns like:
Position; Month (I advice to use format like 2022.09), and optionally [WeekdayNo]; [DayNo]
To get Position for Employee, you also need am Employees table, with columns for employee and it's Position (in case the position of employee can change over time, you must have instead Employees table, an EmployeePositions table with columns for Employee, Position, and PositionDate, and probably a hidden sheet with table, where current position for every employee is listed)
You can also add a calendary sheet, and a holidays sheet (or have a column in calendary sheet for holidays) - to use in calculations (e.g. to determine, is the date workday or not).

And then you can create a Report sheet, where user selects School and MonthNo, and the table like in School sheets of your example workbook is filled with data from data entry sheet.

As result, your workbook will have sheets for data entry, for Schools registry (your Top table), for Employees registr(y/ies), and a single report sheet. To add new schools in future, you simply have to add them into Schools registry, and you can start to enter any needed data for new school into data entry table.