Set the Instant Pot to Sauté and heat the olive oil until shimmering.
Add the diced onion and cook, stirring occasionally, until softened, about 3–4 minutes.
Add the minced garlic and sauté for about 30–60 seconds until fragrant.
Pour in the chicken stock (or pineapple juice), salsa verde, and honey, and scrape the pot bottom to release any browned bits.
Submerge the chicken breasts in the sauce and sprinkle with salt. Secure the lid and set the valve to sealing.
Cook on High pressure according to chicken state and size: fresh small (6 oz) breasts 6 minutes, fresh large (8–10 oz) breasts 8 minutes; frozen small 10 minutes, frozen large 12 minutes.
When the cook time ends, allow a natural pressure release for 10 minutes, then quick-release any remaining pressure.
Open the lid, shred the chicken directly in the salsa verde liquid with two forks to keep it moist.
Stir in the lime juice, if using, taste and adjust seasoning, then serve or use as desired.