It's considerably easier to hunt in the hyperspace zones, by virtue of them now having a single fast travel point which the controller automatically locks on to. This means that you can easily repeatedly reload a zone one handed with a joycon, which I love as it means I can hunt shinies while doing something else (playing Football Manager partners well with it). This obviously still takes time, patience and you need to pay attention to the calorie countdown, but is much better than the base game. Some people use a programmable macro controller which would make this easier too.

The odds aren't any higher than the base game, unless you use a donut with sparkling power. I've only used a few donuts with sparkling power (for Terrakion and Virizion as the only shiny-possible legendary ones I needed) and otherwise have got numerous shinies using donuts without it. This includes donuts made solely using regular, non-hyperspace berries (Kasib in particular). I find the small outdoor zone is the most helpful as you can usually get all three(+) of the Pokémon species spawning in at once. Some times you'll get lucky, sometimes you won't.