In-universe examples of UFP spying?

[Christopher]

As Idran said above, I took it to be a fleetwide project.

My bad. I must have missed that.

Well, I don't think they said as much in the movie itself; it's just implied by the fact that both ships have the equipment onboard.

Enterprise wasn't in the same area and didn't seem to have a specific mission like Excelsior did, so I don't agree, but to each their own. I'll just go with Davd Mack's explanation

Well, a fleetwide project to chart gaseous anomalies would presumably cover all of known space, not just a single area. And as I said, I doubt the Excelsior would've spent three whole years doing nothing but that. It seems more like a "whenever you can get around to it between bigger projects" kind of deal. Or a standing research order like the quasar survey thing from "The Galileo Seven" (which was apparently important enough for Kirk to delay delivering vital relief supplies just so he could follow the standing order).

 

[David cgc]

^Uhura was on the Enterprise. Sulu was on the Excelsior. Am I missing something?

No, you're not — the writer and director of the film did. They established at the start of the film that Excelsior had such equipment aboard — then they had Uhura reference it during the climactic battle sequence, as if they had said the gear was on the Enterprise all along. I suspect that's the kind of error that occurs either because of a last-second rewrite with a poor continuity check, or an on-set change that no one caught.

There's a deleted scene in the script where we actually see the tour Kirk takes Gorkon's party on before dinner, and they pass through the science lab and Kirk mentions that all of Starfleet has been on the lookout for gaseous anomalies recently and all ships are carrying specialized scientific equipment for that project.

The only reason it exists is to set up the end of the movie, and it telegraphs it fairly obviously, so I can see why it was cut. The only thing we see of the tour is the science lab, where Kirk mentions gaseous anomalies, for the second time in the movie. It'd make it too obvious it was going to be important later, like when an action film has a TV on in the background in the first act mentioning they're about to demolish the abandoned power plant in town, to set up the location of the final fight. And since it's just everyone gawking at the gas sniffer for a second, it doesn't establish any other plot or character information to justify breaking the pacing up between the arrival and the dinner. Maybe if it was part of a larger tour sequence, where the gaseous anomaly line is slipped in amongst showing something that's more obviously interesting to the audience, like the Klingons' reaction to the bridge or sickbay, but it wasn't written that way.