This is wrong, the number of transactions has (almost) nothing to do with the energy usage. I wrote almost in brackets because the transaction fees contribute slightly to the total compensation of the miners. So it is mostly the block reward that determines the energy usage (for now)
I can veryfy all Bitcoin transactions ever happened on the network on my laptop in a few days, I'm sure it's less than that, my Apple M1 laptop is quite energy efficient.
New blocks are created with transactions in them and can’t be verified if they haven’t been mined, because verification works by checking the hash that the miner found.
Transactions that are not yet part of a mined block cannot be verified.
What you wrote is all correct. Just don’t confuse creating the transaction and adding to the network (which is relatively expensive) with verifying (which is cheap, an SHA-256 hash can be computed in 2 days by a human with pen and paper, and for verifying the transaction you need an exponentiation on an elliptic curve, which is still efficient, though slower).