How can I see my Apple Pay transaction history on my Windows PC?

The only way I know of on a PC (and what I do myself) is log into chase.com and view transactions there -- Apple Pay with a Chase card is just another way of using the card (e.g., in-person swipe, in-person tap, online, etc) and they don't separate the transactions by how they were originated.

You can use any internet browser and go to https://card.apple.com/ to see Apple Card statements but there is no option to see recent transactions that have not yet appeared on a statement.