One can, fairly easily, create a horizontal document with binding on the long edge to allow vertical flipping of pages with InDesign. It merely requires one to think a bit different about the overall configuration/set up of document pages and their contents.
Merely rotate the horizontal contents of a page so it's vertical. Or set up a vertical document and then use the page display options to display the pages rotated 90°.
Basically, set up a vertical book with the page contents rotated. That allows you to use the "print booklet" command and get a landscape book.
For Clarity....
This will use non-facing pages that are set in spreads, but it works the same for facing pages. Here is a standard configuration for a traditional saddle-stitched book:

The stitching occurs on the long edge.
Problem: The contents of the pages are vertical. The desire is to have the contents running horizontal, but keep stitching on the long edge, so the final stitched booklet will flip vertically, like a calendar. Like so...

https://www.presentermedia.com/powerpoint-animation/custom-calendar-flip-pid-19010
Note the binding, in this case ring binding, is on the long edge. So that's what you need to accomplish with the set up.
In InDesign, highlight the spread in the Pages Panel and from the Pages Panel menu, choose Page Attributes > Rotate Spread View > 90° CW

This will rotate what you see and not any aspect of the layout or construction. This merely shows you a rotated preview rather than the actual vertical preview.

Note the Pages Panel above - the spreads are all still vertical but there's a little "rotate" icon next to the spread to indicate you are viewing it rotated.
Now, simply rotate the page contents to match the spread rotation...

You can then output this file like any standard booklet set up and it will be bound on the long edge and allow for the "calendar-like" flipping vertical.
For demonstration purposes, you can remove the preview rotation at any time by choosing Page Attributes > Rotate Spread View > Clear Rotation
from the Pages Panel menu...

And you're back to a standard preview, but now the contents of pages are rotated to match the desired output:

Note that you don't need to remove the rotation once it's been implemented. It's fine to leave the spreads with the rotated preview, they will still output as if they were vertical.
This is all simply a way to alter what you see in order to work more efficiently but still allow standard vertical output in order to allow the "print booklet" command to create a proper PDF for saddle stitching.
If the desire is to have binding on the short edge, there's no need for any custom set up with respect to binding. Merely create document pages which are wider than they are tall. Issues may arise here due to limitations of any output/bindery device - but the "print booklet" command will still create a PDF with anticipated binding on the short edge. For more clarity here, see the answer from @Wolff, where he addresses possible issues with short edge binding.