When was the butterfly keyboard introduced to the MacBook Air?

I assume you're trying to avoid purchasing a model with a keyboard that is prone to errors. Apple's "Keyboard Service Program" for the MacBook Air lists the MacBook Air Late 2018 and Mid 2019 models as eligible.

The Mid 2017 MacBook Air and older have the old scissor-style keyboard.

The Late 2018 MacBook Air has the new butterfly style keyboard. It has the newer version of the butterfly style keyboard that has a membrane to keep dust from jamming the keys (as compared to older MacBook Pros that featured a butterfly style keyboard without that membrane). So does the Mid 2019 model.

The butterfly keyboard was introduced to the MacBook Air with the 2018 models.

Models before that had keyboards that were referred to as 'chiclet' type keyboards.

One of the best resources for giving the differences between model generations is everymac.com

This is the entry for the 2018 model that first refers to the "butterfly" keyboard.

https://everymac.com/systems/apple/macbook-air/macbook-air-retina-faq/differences-between-macbook-air-late-2018-models.html

This is the entry for the 2017 model that still refers to the 'chiclet' style keyboard.

https://everymac.com/systems/apple/macbook-air/macbook-air-faq/differences-between-macbook-air-early-2015-models.html

Note: The references to the 2015 model are because they are essentially the same model with a new processor.

To construct a definitive list you should check every model for references to the keyboard, although from memory I don't recall them switching from 'chiclet' to 'butterfly' then back to 'chiclet' and then back to 'butterfly' so if you don't want to read every model then it's probably safe to assume the 2018 'butterfly' was the first MacBook Air to use the new keyboard, although obviously they did appear on the now abandoned lightweight MacBooks earlier than that.