The M-03? It goes to Kharkiv. And to the south it goes to Slovyansk, also in Ukranian hands. I don't see it as a major supply route until you get very close to Izium. I think they're more focused on Kupyansk. If they can take it they can move down the Oskil River and cut off Izium. They can also threaten one of the supply routes to Severodonetsk and Lysychansk.
The Balakliya news is very encouraging. It's a real town (25-30k population) with some road, rail and river access. A definite step up from the villages they took near Kherson. That plus the reports of attacking villages on two roads to Kupyansk make it sound like the start of a legitimate small-scale offensive. Let's hope for confirmation and reports of further progress over the next few days.