Both sibling comments are completely correct, and support the parent comment (thanks!).

I got myself mixed up and was misled by a Corporate Finance Institute quote (which incorrectly notes the loss is unlimited only to contradict itself):

For the seller of a put option, things are reversed. Their potential profit is limited to the premium received for writing the put. Their potential loss is unlimited – equal to the amount by which the market price is below the option strike price, times the number of options sold.