There is no more BTC created after 21 million coins, but the mining continues. This just means that each block no longer comes with a fixed reward, but the miners will still make money from transaction fees.

As far as I understand, the process of mining is verifying the transactions as well. The miners are generating bitcoin as part of the process of verifying the transactions. After the 21 mil limit is hit, they will be rewarded from the transaction fees. (Someone with more in depth knowledge feel free to correct me if I am wrong).

You're not wrong. They currently get the block reward and the transaction fees. When there's no more reward to be had they will get just the transaction fees.

They do verify transactions, and are incentivized to do so by transaction fees

They don't verify transactions actually. That is what nodes do. They retrieve valid transactions from nodes, order them, and then hash them according to the consensus proof-of-work algorithm, which in this case, is SHA-256, until it produces a block that will satisfy the node consensus requirements.

Miners are nodes and therefore verifying transactions, and they're the only nodes writing transactions to the blockchain.

Non-mining nodes can only verify transactions for themselves , which helps them stay on the chain of their choice but does not extend any chain.

Miners require nodes, so they have them too, because without nodes they can't source transactions. Every node, applying consensus rules, extends the blockchain by accepting valid blocks that meet consensus rules.

We have had a year long education in the limited power of miners with many people incorrectly attributing responsibility for maintaining the protocol. Miners were rightly shown to be powerless to force consensus changes on the nodes. When push came to shove they did what they were told, at the threat of being crushed with a pow change.