for each Kagi search they hit APIs of other search providers etc., so they need to cover that cost.

Except for these types of services scale is in your favour. A bakery has a high cost of goods sold, whereas services like this tend to have high fixed costs but relatively light costs per customer. So scale is very much to your advantage (within reason).

because they have to pay for queries to other APIs for each search, COGS is relatively high I think, which is counterintuitive for a web product like this.

my sense is their fixed costs are relatively low.

It if supporting each customer costs them, say, $2.50