Closing-Off a period allows you to protect the records, prior to the close-off date, from being added to or changed and thereby causing historical reports to differ, if the same report was run again at a later date.

It is an odd quirk of the PHM program that the date for the 'Close-off Period' must be the first day of the 'Next' period, that is, to not allow any further entries up to the end of May, you will enter in a Close-off date of 1.6.2022. I have no idea why and to change it now may cause more problems for existing clients who are used to the anomaly.

For reporting using the 'As At...' reports, you will use the date as at the end of the reporting period.  So, YES, to report to the end of May, for the 'Total Stock Cost As At Date report',  you will use the date of 31.5.2022.  The report looks for all entries recorded prior to the last second in that period.