The industry standard tests are ANSI standards 42, 53, and 401. 42 addresses contaminants that aren't health related (chlorine, particulates, etc), 53 addresses contaminants that affect health (lead, VOCs, asbestos, etc), and 401 addresses "emerging compounds" which are things like prescription drugs, pesticides, and other incidental things whose effects are still being discovered.

Most good filters will be certified for several of the more common contaminants from these standards, Brita Elite and Longlast+ filters are certified for 13 of the contaminants in Standard 53. You can find this on Brita's performance data sheet, and Pur has similar info available

The difficulty is because there are so many different contaminants that testing and certification becomes really expensive and convoluted. Just because a filter has an NSF certification doesn't mean that it's certified to filter the specific contaminant you're looking for.

Then you get into sketchy stuff like Berkey and other rando filters where getting certified for all the containments they claim would cost over a million dollars, so there isn't really a way to verify their performance figures except running an independent test for hundreds of chemicals.