Sweet Peppers in *Oregon, interesting. Gives me some ideas about TTL Western North America.
That's probably more than me - I haven't really worked out yet what will be happening with the Pacific Northwest ITTL. (*California, yes, sort of. *Oregon, not really.)
That said, sweet peppers will grow fairly widely throughout the cool temperate zone. Eventually. Once people have worked out (or found Aururian experts to teach them) how to farm in a way which fits their peculiarities. For instance, in their natural habitat sweet peppers are alpine rainforest crops, i.e. they need high rainfall, and not too much heat. They are also understorey plants, mostly growing in areas of partial light. They can be sensitive to too much light (well, mostly heat), which can be bad for them.
A few particular regions already pretty much naturally have these conditions, and these will probably be the first to take up cultivation of sweet peppers. In OTL, one species of sweet peppers grows wild in Cornwall (where it was imported from Australia). ITTL, Brittany, which has a similar climate, will be an early cultivater of sweet peppers, making them even more wealthy than they were in OTL.
Other areas will also cultivate sweet peppers once they work out how to mimic the natural conditions - principally, grow the plants in enough shade that they can cope with the heat, and frequent irrigation at the right times of year (spring, autumn).
While on the subject of the Maori, we know they have gotten ducks,quolls,emus (and maybe geese?) from Australia. Have they started raising any livestock from Europe or Asia yet?
Occasional imports of donkeys, horses and cattle, but on a much smaller scale than in *Australia. Aotearoa is further to sail, which makes obtaining livestock even more difficult, and trade has been much more limited. It's entirely possible that the first Māori exposure to European livestock will actually be supplied by the Islanders trading livestock born in Aururia. Pigs and chickens have been brought in from Polynesia at some point, too.
Also, what wild species have been introduced into New Zealand (accidentally or on purpose)?
So far, very few. Trade has been so limited, and wild species aren't really high on the list. Pigs, cats, more breeds of dogs, horses, donkeys and so forth, yes. Wild species, not so much. The only ones which are definitely there are rats.