I wondered if anyone could tell me the feasibility of developing a Chrome extension that could collect microdonations at the checkout?

It could work a little like Moneybox here in the UK or Acorns over in the US, which collect micropayments on purchases via "rounding up" and put them in a savings account.

For example a pop up may ask before payment is made, "Would you like to plant a tree for $1 with this purchase?"

People feel richer on different days to others I guess, so it may not get annoying. It could share the donation confirmation page on Facebook after. One Tree Planted https://onetreeplanted.org/ could plug in to it, or you could choose from a list of charities the user feels an affinity with.