Steps to reproduce the issue

2 way to reproduce
i.e to test you can pick an article from admin site and go on tab "publishing"

First:
Choose a field with existing date where you can open a calendar picker (front or back end)
Click on the calendar icon to open the picker
Modify the hour from the field itself with the keyboard, not with the time picker
Click outside the picker (not close button)
Don't re-select the field, click on "save", the hour hasn't been modified

Second:
Choose a field where you can open a calendar picker (front or back end)
Click on the calendar icon to open the picker
Select a day from the picker
Modify the hour from the field itself with the keyboard, not with the time picker
Click on close button (or outside the picker, same result)
Don't re-select the field, click on "save", the hour hasn't been modified

Expected result

The time should be updated with the values the user sees on the field

Actual result

The time goes back to old values on save, it's annoying for users using Icagenda, the don't understand why the hour is wrong time to times

System information (as much as possible)

Tried on 5.3.0 version and on a new fresh Joomla 5.3.2 same result
Tried on a different server same result
PHP 8.1 all requirements from Joomla respected

Additional comments

Same on front end or back end
The behavior is a little bit different if select a day or not after opening the picker.
If you don't select a day with the picker and change the time within the field, clicking close button is ok.
If you pick a day (like when the field is empty) then changing the time within the field and clicking close is not okay

What I understood is the form keeps the data of the calendar picker but the view is only showing your modifications.
That's why if you select the field after closing the picker, the form is updated with the rights values when you unfocus the field