It's the prof modifiers to danage. Its a pita to keep track seeing a player struggle (theyre 14 1 session played with feat).
You confused me now. Are we talking about Cleave or Great Weapon Master or both?
If it's Cleave, then your proficiency modifier doesn't matter because you don't add them to your damage roll anyway. You only add your ability modifier to damage rolls, except when it's the Cleave attack against the second creature because the Weapon Mastery property says so.
If it's Great Weapon Master, then yes, you add your proficiency modifier to the damage roll of attacks made with the attack action, but not bonus action attacks, opportunity attacks, or attacks made as part of the Magic Action, like when casting True Strike or Booming Blade and you're not an Eldritch Knight who replaces one attack with casting a Wizard cantrip as part of the Attack Action with War Magic.
Or do you mean a combination of both? Cleave when you have Great Weapon Master?
If so, this is indeed a bit more complicated, but I'd say no. Great Weapon Master says that the attack has to be made as part of the Attack Action and the Cleave Mastery Property does not say that the attack against the second is made
as part of the same action like the Nick property says. Such wording is missing here. Also, the Cleave Mastery Property says that the target takes the weapon's damage, meaning just that and nothing else. Unlike spells like Conjure Minor Elementals, which say something like "any attack you make", so the damage could be added to the Cleave attack against the second creature, there is nothing regarding Great Weapon Master that could override the wording "takes the weapon's damage" like the wording of Conjure Minor Elementals does.
However, personally, I consider this an oversight as it is only missing a wording such as
"as part of the same action, bonus action, or reaction" to make this applicable and I would homebrew this, so that the extra damage from Great Weapon Master applies to the Cleave attack against the second creature if the attack against the first creature was made as part of the attack action. And if it's your table and I were you, I'd make that ruling in favor of the player in that case. But I always rule in favor of the player in such cases, so you could call me biased. Quite honestly, if one of my players didn't go ahead now and create an Eldritch Knight and then Cleaved with True Strike as part of the Attack Action through War Magic and with Great Weapon Master, I'd be disappointed, but if they did, they'd get all the damage minus the ability modifier because that's cool and clever. And Rule of Cool is my jam.