The reverse is probably going to be true, unfortunately. The F16s weaponry is still based on 70s/80s engagement envelopes, more modern Russian a/c use missiles/radar that have much further range. The F16s will be most effective where UKR has additional anti-air assets to keep the more modern a/c away.
A very good breakdown of this by someone who's studied military aircraft for a living...
https://xxtomcooperxx.substack.com/p/its-the-range-stupid-part-1
https://xxtomcooperxx.substack.com/p/its-the-range-stupid-part-2
https://xxtomcooperxx.substack.com/p/q-and-a-regarding-f-16s-for-ukraine
https://xxtomcooperxx.substack.com/p/q-and-a-regarding-f-16s-for-ukraine-51d
https://xxtomcooperxx.substack.com/p/q-and-a-regarding-f-16-for-ukraine
You had said "Allegedly they can shoot down Russian planes, because their targeting systems have longer range."
My post was to share information to indicate that is not so - F16 does not have longer range.
The rest, you and Tom are in agreement.