I am in the market for a Ring doorbell and was googling on how to find a doorbell transformer. I believe I have found it - but it’s attached to the furnace switch.

The wires connected to the transformer are skinny and sticking out from the wall (a sign that this could be the doorbell transformer). But to be on the safe side I did the following test: Remove one wire from the transformer and test the doorbell and the furnace - when I switch on the Power to the furnace the furnace light turns on AND when I pressed the doorbell button the doorbell stayed silent. I put the wire back onto the transformer, and the doorbell start singing again.

The transformer shows 5va- 10v so this is way underpowered - How do I replace this transformer? Or would the Ring bypass option work?