When selecting a Date & Time using the DateTime picker, the Time Picker's _removeModal function removes event listeners that it shouldn't be. This causes elements like the sidenav toggler to stop working.
Using a Date format that uses a month string, rather than a number (i.e. 'dd mmm yyyy'), causes the browser console to throw errors whenever the Date/Time value is changed manually with the keyboard.
Uncaught TypeError: Cannot read properties of undefined (reading 'findIndex')
Probably a symptom of issue number 2, but changing the Date/Time with the keyboard doesn't re-set the correct Date/Time. This means that when re-opening the picker, the incorrect Date/Time is selected.
Using the regular Time Picker also "breaks" the sidenav toggler.
The regular Date Picker doesn't suffer from issues number 2 or 3.