This is similar to another question this morning to search json responses. The solution is the same, star this issuethis issue. Starring is triggered via the star icon in the far left area of the blue title are just under search.
Starring issues let's the developers know what people need. The more stars something has, the more likely it is to get worked on sooner.
Currently this functionality is not provided and extensions are unable to add this type of functionality since the network panel isn't extensible in this way.
Inspector of Microsoft Edge browser offer such feature. Useful when you need to search through traffic made by an HTTPS web site that Fiddler cannot inspect (like Facebook web site).
Edit: I believe this was working for all resources at the time of writing, but please see comments because people say it is not/no-longer working as expected.
As of Chrome version 91, if you want to search through all resources (not just AJAX/fetched resources), then you need to open DevTools and then press Ctrl+Shift+F to open a search box. If you just type into the "filter" text input then it only searches through the URLs, rather than also searching the contents.