When can I book?
This seems to be somewhat variable as the testing process is still ongoing, but at present you can book up to 27 days before the planned date of your meal. So for example on August 1st you can book a meal time for August 28th.
The system currently only allows you to make a pre-booking within the first SEVEN days of your hotel stay, and those dates will still only open up one day at a time (there is no "arrival date plus 10" system like there is with ADRs). So if you are arriving on August 28th, then on August 1st you can book for your first day, on August 2nd you can book for your second day, on August 3rd for the third day, etc., up to a maximum of seven days into your stay.
If you want to book for some time later within a longer stay, this only becomes possible after your hotel arrival date. On your arrival day you will be able to book for day eight, on your second day for day nine, etc.
Note: the system will start displaying all seven of your possible booking dates as soon as you have linked your reservation details. However if you try to make any booking before that 27 day window you will be shown a message saying there is "no availability". Do not be concerned about this wording, it does not mean the restaurant is sold out, just that your booking window is not open yet.