F-16 is no more “nuclear-capable” than existing Ukrainian aircraft or artillery (actually - the artillery actually IS capable - just need the munitions).
Not true at all. Aircraft such as the F16, F15, F18, F35, F117, F22 that drop tactical weapons are dual purpose when they have the encryption key panel installed. This enables command control authority starting with the Commander In Chief down to the military command authority down to the squadron CO down to the the pilot for all nuclear weapons including gravity dropped tactical weapons. The correct code must be entered or the weapon will not arm. Too many incorrect code entry attempts and weapon disables itself. Not all all fighter squadrons and or aircraft even have the key encryption panels installed. Plus these aircraft have the targeting computers for an over the shoulder release of the weapon starting at low level from the IP or high level drop with time for the aircraft to safely bugout, so not all aircraft even have correct avionic configurations. I doubt the Ukrainian aircraft have any of this capability at all and should not our would not to start with.
Russia is correct to be concerned that a nuclear capable delivery system is minutes from their border and would take actions to remove them just like we threatened to do to Cuba in 1962. Regardless that we have stealth bombers and tactical stealth fighters that can already penetrate their airspace undetected. But, to Russia this is an existential threat out in the open and we are idiots for not listening to their red line. Sempre Fi.