The Sassanids need to either coordinate armies around both sides of the Black Sea ( very difficult if not ASB) or they need to figure out what the Ottomans finally figured out 900 years later--that to defeat the ERE, one needs to take over all the land from which their armies are levied. And that means NOT getting bogged down in a siege of Constantinople, but using whatever navy and barges one can put together to invade Thrace, Greece and Moesia BEHIND Constantinople leaving Constantinople a city state behind the Wall of Theodosius. The Ottomans consolidated their European Empire for 100 years after the Battle of Nicapolis before finally investing Constantinople.
If the Sassanids do this--and make peace with the Avars--not even Heraclitus will be able to save the Empire by sending an Army to Azerbijan since he will not have anywhere to levy such an army from.
And as for Rome, making peace with the Avars may mean letting the Avars have Italia. And Francia if the Avars can take it. Khosrau does need to know when and where to quit.