Two problems.

1) Russia would love Belgorod threatened it would be evidence of Ukraine's 'evil intent' and would rally the Russian people.
2) ultimately, Putin doesn't care about the north but has built his whole reputation on Crimea. It has been clear since 2014 that he doesn't give two hoots about lugansk and donbas, these are just spoiler regions to annoy Ukraine. You want to stop the war? Attack or threaten(be in position to attack) to attack Crimea. Putin cares about nothing else.