I'm reposting this information with this new title, since it looks like at least 4 others besides me were having trouble with Helix 2 displaying the off-canvas menu properly, with dropdowns. This is the final summary of what worked for me:

Here's the process I followed to get the off-canvas menu to display with the drop-downs, in case this can be useful for anyone else:

TURN OFF the "Off-Canvas" module published in the "off canvas" position. (This seems to be an artifact of Helix 1, that interferes with the display and functioning of the off-canvas menu in Helix 2. )

UPDATE the Helix template (currently, to 2.0.5 - I'd previously been on 1.1.4.)

SELECT a layout setting for the Off-Canvas menu, in the Helix template settings. (I chose Left Aligned.) Make sure you hit "Save" (top right) after selecting your option - otherwise it won't have any impact. Apparently in Helix 2 you have to choose one of these 3 layouts in order for the off-canvas menu to display at all.

Other fixes if needed:

CLEAN UP menu item type in the main menu for parent items. (For some reason, mine were displaying as "URL" - I changed them to "Menu Header". This proved not to be needed for the dropdowns to display OK - but it is a better setting for SEO clarity)

CLEAN THE CACHE - on desktop, on each individual mobile device, and in the global Joomla cache. This was not necessary in my 2nd site - but was crucial, multiple times, on my first site, to see the changes from items 1-3.

Hopefully these hard-won insights can help somebody else facing similar difficulties. And hopefully, can help tag improvements needed for future Helix updates.

( (I personally think in future updates, the off-canvas menu should default to a functioning layout, with the option to change it later if desired - rather than not have the menu display at all until you choose one. Also, in future updates, perhaps it would be wise to deactivate the off-canvas module created from prior versions of Helix, since it seems to interfere with Helix 2 display. Just a thought for the team moving forward.)

PS - now that it's finally working, the Helix 2 off-canvas menu is truly beautiful! Worth the trouble. Hopefully easier to achieve now, with these observations. Hope this can be helpful for others.

(If you want to reference the original post, for how these fixes were revealed, you can find it at the end of this page: https://www.joomshaper.com/forum/question/9103