That could very easily be done with all of the logic in Glide and no formulas in the Excel sheet. In addition to the slowness, you are also restricting yourself to only one user using your app at a time by having the logic in your Excel sheet.
All you really need is to have a checkout table with two user specific date columns. You can use a date time picker to write dates and times into those user specific columns.
In your Cars table, add two single value columns to bring both of those dates into the Cars table. Then create a Query column that points to the Agenda table, with a filter that matches where Car is Row → Car, Start Date is before Row → End Date, and End Date is after Row → Start Date.
Then you can set you cars collection to only show if the query column is empty.