Is there a way to verify how many Liquid Bitcoins are in existence? Is there a way to recognize peginaddresses where bitcoins are locked up for use on the Liquid sidechain, and therefore a way to sum up the total bitcoins currently circulating on Liquid?
You can easily verify the liquid circulation, in fact any liquid node can do this in realtime as part of its operation if you run a Bitcoin node along side it.

Pegins can't, however, be reconized until after they're claimed on the sidechain.  Before then the addresses are cryptographically indistinguishable from other similar multisig transactions on Bitcoin. But when they are released into the sidechain the party that generated the address publishes the information needed for everyone to find them.

https://liquid.horse/ is a website that runs a liquid node and reports this sort of data.