every source you read will say that bitcoin mining costs are going up.
That's correct. The price of BTC increased and the Bitcoin fees increased, so the value of the block reward + the transaction fees (what miners receive when they mine a block) increased.
Because of this, more miners piled in to join the "lottery" and try to mine a block. At the next difficulty adjustment (a difficulty adjustment occurs every 2016 blocks), how difficult it is to mine a block is altered in order to ensure that a block is still mined approximately every 10 minutes.
The mining costs are going up
because the price is going up. Correlation != causation.
I actually didn't see a single piece of evidence that shows bitcoin prices and mining costs aren't correlated.
Exactly. They are correlated because if the Bitcoin price increases, the reward for miners in fiat terms when mining a block increases.
Not the other way around.
You would actually have to use quantitative modeling to prove it and not just spitting out bullshit.
Nope, you'd have to read about how Bitcoin works.