When opened in Publisher 2, on MacOS (m2), this works fine, even if the overall process I still think could be improved. But I have no issue tabbing/shift + tabbing to change the indent level.
When I take the same document (reopening without saving any of the changes) and open it directly into Designer 2, the same tabbing/shift + tabbing doesn't work. It only creates another list item of the same 'level', and any tabbing just adds a tab at the start of the item value (after the bullet/number, before the text).
I see you have an M1 ipad, I'm not sure that the same problem would appear on iOS but might be worth a check.
it does feel like I had it briefly working in Designer after a lot of screwing around, before trying to add a third bullet level, but I honestly can't remember if it was in Designer or Publisher...I went to dinner and put the kid in bed in the intervening time.
EDIT: I also just created a new blank document in Publisher, which has a default set of Text Styles (which I guess are pretty much the same as in your document) and got the same behavior i described above. Works in Publisher, then moving it into Designer breaks it. I'm going to see if I can get someone in the Discord server to replicate with a Mac.
ONE MORE EDIT: When I recreated all the styles/rules again, entirely in Designer 2, it wouldn't work in Designer when I was testing it. But I persevered, and moved to editing the document in Publisher 2. In Pub, the Text Styles all worked perfectly, with tabbing to the next levels working just as expected. Switch back to Des, and again no longer working. So I'm just pretty confident it's a bug.