This isn't quite right. The max number of bitcoins is just based on the number of times you can subdivide a 64-bit floating point number. There's some technical spot in the design where this matters.

The complexity of the algorithm can be scaled up and down pretty arbitrarily, and it's adjusted block-to-block based on some formula in order to keep the average time to solve the algorithm worldwide at 10 minutes. Literally they just change how many digits of the right answer you need for it to be accepted, and I think currently you have to match the least 44 bits of a 256-bit number or something.

I don't remember how the hashing algorithm works exactly, but the basic idea is that it's very easy to determine if the answer is right or wrong, but you can only guess and check. I think there's a 3Blue1Brown video that explains in depth.

The relationship with mining is that the reward for adding a block to the ledger decreases as more bitcoins are added. This was just an arbitrary formula chosen to eventually reach a zero reward before it hit the max number of bitcoins. The only way new bitcoins are created is as a reward for solving the blockchain algorithm and adding a new block to the chain.

The reward isn't the only way miners are paid, though. The size of each bitcoin ledger block is fixed, and can only hold so many transactions (and there's one new block every 10 minutes because of the difficulty scaling). There are very often more people who want to make new transactions in ten minutes than there is room in a block. So when you initiate a bitcoin transfer you can add a bribe for miners to prioritize your transaction. Whoever puts your transaction on the blockchain gets your bribe money (in bitcoins, obviously).

Once the mining reward hits zero, miners will only mine because of bribe money, which the advocates describe as a smooth transition to a system of Market Rate™ transaction cost. But of course it's still deflationary by design.

And by any actual monetary theory accepted by literally anyone but the absolute craziest far-right goldbug whackjobs, you would want new currency to be generated forever so that it's constantly depreciating in value. Inflation is good.