Where exactly does bid/ask price come from?

All I can find online is the definition that “bid price is the highest price someone is willing to buy for and ask price is the lowest price someone is willing to sell for”, but how exactly does this mechanism work in the brokerage? Where exactly do these numbers come from? I would have assumed that the bid/ask price is determined by limit order limits, but that does not seem to be the case? If someone places a limit order above the highest bid or below the lowest ask, the order would simply be treated as a market order, instead of raising the bid or lowering the ask. Then where do bid/ask prices come from if they are not based on limit orders? Thank you all in advance, I really can’t wrap my head around this lol.