It is subtle, but PoW mining itself doesn't generate coins. It isn't like someone is digging a hole in the ground and extracting gold.

PoW miners are rewarded for correctly validating transactions, with newly minted coins.

The whole proof of work thing is that you proved that you validated a transaction by expending energy, and the network pays you for that security service.

Miners then need to sell those coins on the open market in order to pay for their capex/opex, which creates the market.

The open question is that if you have a fixed supply of coins that eventually runs out, what will carry the miners?

It'll be increased fees or the network will switch to another solution.

Agreed with your explanation.

I would add a different way to make sense of it.

Proof of work allows for what Keynes called "Bancor". BTC is succesful because unlike fiat central banks, the money supply isn't dictated by interest rates (and thus loans) but by the effort of participants. The price of BTC is almost irrelevant, BTC itself is a paradigm shift.

Regarding the fixed supply, it's only fixed because participants agree to the consensus algorithm that fixes it. Many cryptocurrencies have different tokenomics, such as ETH's rules under PoS. BTC miners could vote onchain for a hard fork to change the 21M cap - or another solution.

I believe transactions are quite optional though? A miner could choose to mine empty blocks if they truly wanted, which transactions to include if any is up to them.