A lot of PBN’s use expired domains, if the links to the website appear to be dodgy or just not makes sense then it’s likely that it’s part of a pbn, you can also check in archive.org
Estimate Traffic Data
You can also use the regular SEO tools like ahrefs, semrush etc to see if they think the site is getting any real traffic. This data along with their proprietary metrics like DR can paint a strong picture.
The design, or lack there of can be a major clue to as to whether the site is a PBN or not.
The quality of the content on a site will go a long way to telling you if it’s a pbn or not.
Also check if the outbound links have a pattern to them, and in turn do the sites they link to also link to the same websites.
Check if the author of the content is real, if there is no author then this can also be a red flag. The lack of an about us or a contact page is another sign that the site might be a PBN
The reality is however a really good PBN will be very difficult to detect.