Location of saved files in Safari private browsing mode?

I was on Safari private browsing mode on my iPhone and I clicked on a pdf download link and it started loading and then opened the pdf within Safari itself. Supposedly it was a download link and now I cannot find the pdf file anywhere in my local iPhone file nor in iCloud. Where are files downloaded in Safari private mode saved or does the private mode block downloads or something? If so, did I end up downloading nothing? Chatgpt told me that private mode doesn't write to disk but only temporarily saves the files in ram and deletes them when you close the session. But since its information is from 2021 I wanted to check here to get a reliable answer.