I’ve had cause to find vegetarian dishes from different eras and its surprisingly easy. As you say, vegetarian (traditional ovo-lacto) was the default diet for many people simply due to cost and there were vegetarian dishes on the tables of the wealthy served alongside meat dishes.
Chestnuts and mushrooms were forageable and featured in Autumn stews/puddings along with whatever other vegetables were available so it wasn’t a bad choice for a “regency pie”. Not sure that the pasta would have been a likely sight.
I also hate the term “plant based” which has no more meaning than “flexitarian”. If she is vegan there is already a term for it. I also dislike the fake meat which is taking over the precious few menu slots for non meat eaters. I thought the fake pork was just pointless but the Heston challenge did actually ask for “fake”.
I’ve never been to his restaurant but I know a couple of people who have been for the tasting menu and who said the whole experience was incredible and that the overall effect of the dishes doesn’t come across on a tv show.