Is Civibooking compatible with PHP 7?
I would suggest you try it out whether it works on PHP7. And if you find out it breaks you have two options: 


Fix it yourself (if you are a developer) and push a Pull request to the original developer
The other option you have is that you pay a developer to fix CiviBooking.


There is also a third option and that is to ask around in the community whether there are other people willing to contribute to make CiviBooking compatible with PHP 7.

I have one last remark, PHP, CiviCRM are all open source. So there is no supplier who guarantees that stuff keeps working. The End of support of PHP5x does actually not mean a lot, it means that the original developers of php5 will not bring out any new (security) releases of that php version. But others might still do that and no one prevents you to fix your php yourself when you discover a security flaw. 

One really last remark, you said you depend on CiviBooking. The other option you have is not to upgrade php 5 to 7 as it brings in a risk for continuity of your primary process in your organization. But if you do not upgrade you have another risk and that is that your php 5 might become insecure at some point in the future.