I’m unaware of any method to directly open puzzles in my private collection. I know a slightly circuitous method: open a particular collection, click ‘edit’ on one of the puzzles from the collection, and from the edit screen I am somehow able to (I can’t remember the specifics, not at a desktop ATM) start playing through the puzzles.
I am unable to use this method on my tablet. Tapping the edit button does nothing, and I cannot long press to bring up the menu where I can select “open in background” (i.e. a new tab). I have tried using Safari, Firefox, and Brave. OS and browsers are up to date.