"Private" and "Hours only" events are not considered by appointment

Steps to reproduce

1. Create an appointment calendar and configure it
2. Create an event with privacy set to "Private" or to "Show only hours"
3. Go to appointment page to book a schedule, schedules are still available
4. Create an event with privacy set to "Public"
5. Go to appointment page to book a schedule, schedules are not available

Expected behavior

Private and show only hours should be not available for booking

Actual behaviour

Private and show only hours are available for booking

Calendar app version

3.5.5

CalDAV-clients used

No response

Browser

Firefox 109.0.1

Client operating system

Ubuntu Linux

Server operating system

Debian 10

Web server

Apache

Database engine version

PostgreSQL

PHP engine version

PHP 8.0

Nextcloud version

24.0.7

Updated from an older installed version or fresh install

Updated from an older version

List of activated apps

No response

Nextcloud configuration

No response

Web server error log

No response

Log file

No response

Browser log

No response

Additional info

No response

Reproduce the appointment-booking flow with Private, Show only hours, and Public events using the stated steps. Trace the availability check that distinguishes these privacy settings, then verify that Private and Show only hours events block booking just like Public events.