Steps to reproduce the issue

Joomla 4.2.8-dev with en-GB language and the language overrides to simulate en-US:

DATE_FORMAT_LC4="m-d-Y"
DATE_FORMAT_FILTER_DATETIME="m-d-Y H:i:s"
DATE_FORMAT_CALENDAR_DATE="%m-%d-%Y"
DATE_FORMAT_FILTER_DATE="m-d-Y"
DATE_FORMAT_CALENDAR_DATETIME="%m-%d-%Y %H:%M:%S"

Enable the option Allow User Registration.
Create a user custom field of type Calendar, 'Date Of Birth'.
Go to the front end and select the option 'Create an account' from the login module.
Fill in the registration form but use an existing username.
Fill in the Date Of Birth from the Calendar button, for example 01-31-2023.
Click the Register button to submit the form.
The form is displayed with the error 'The username you entered is not available. Please pick another username.'

Expected result

The date field is displayed as 01-31-2023

Actual result

The date field is displayed as 31-01-2023

System information (as much as possible)

Joomla 4.2.8-dev of 12 February 2023, en-GB, on Wampserver 3.2.9 using PHP 8.1.10 in Windows 11

Additional comments

Reported first and discussed in the Joomla forum at https://forum.joomla.org/viewtopic.php?f=808&t=999269
When a new user is created at the back end using an existing username and the error message "Save failed with the following error: Username in use" is received, the custom date is displayed correctly.