You can use http with Pi-hole v6.
If this is not working you need to check if the web server is using the correct ports. Generate a debug log and we will be able to help you.
This is not available in Pi-hole v6. For security reasons Pi-hole v6 web interface doesn't have permission to execute commands using elevated permissions (sudo is not available), so shutdown or reboot cannot be executed.
You can run Pi-hole v5 in a docker container.
Tag 2024.07.0 is the last image running Pi-hole v5.