They mention in the article that as there is a limited amount of coins that can be mined the mining activity will eventually die down, but as I understand it the verification and validation of transactions happens along with mining.
How will verification work if mining stops? Or will the mining just stop producing new coins but continue being profitable with just the transaction fees?
> ...mining just stop producing new coins but continue being profitable with just the transaction fees?
The profitability of mining never really changes. When rewards for mining increase, profitability briefly increases, but then more miners join, the hash rate goes up, increasing the cost of mining and bringing mining profits back to equilibrium. And vice versa: if rewards for mining were to go down (for example as the block reward reduces according to schedule), the least profitable miners leave, the hash rate goes down, decreasing mining costs and bringing mining profits back to equilibrium.
The hash rate follows total mining rewards (the sum of block rewards and transaction fees). Mining costs follow the hash rate. Mining profitability is the difference between mining costs and mining rewards.
Yes, it is assumed that mining will continue based just on transaction fees. In fact Bitcoin Core almost reached this goal recently due to their hard limit on block size, the percentage of fees in the total Bitcoin Core block reward reached as high as 40% according to the statistics: https://fork.lol/reward/feepct
So with the hard limit there's a set amount of transactions that fit into a block? And whoever wants to get their transaction validated faster can bid a higher fee?
Yes, that is why the transaction fee for BTC has increased in the past (see https://fork.lol/tx/fee), which some people didn't like and argued for a larger block size.
How will verification work if mining stops? Or will the mining just stop producing new coins but continue being profitable with just the transaction fees?