Maybe if we want to give anything for things like fastest pitstop, FLAP, best sector time, best overtake, most overtakes, places gained etc. including pole position laps it should not be something influencing the championship battle, as that is based on race results.
Instead I can imagine trophies, possibly tied with a monetary bonus to help with budgets, given to such achievements.
Maybe have separate “championships/ratings” for FLAPion, Polebeast, overtaking whizz, sector cruncher, pitstopmaniac etc. where some kind of ceremony might be staged at the end of the season / during the winter would be a welcome addition to the season. Indeed, why not introduce something like a real “Rookie of the year” and give an award. It might even help some of these guys to actually stay in F1.
All of that might add to the interest and make drivers go for that extra something to get in the spotlight. But please do not skew the championship battle for that. It would only make the championship more complicated.