I'm not sure that's heat damage. That looks more like cut marks from whittling down the insulation. Right off the bat, if the was was getting hot, so was the lug, and it's completely surrounded by plastic. I would expect obvious plastic damage, not least, just to the right of the lug there's a little metal clippie that holds the plastic down to what looks like a plastic peg; I would expect that to be *totally wrecked*.
I mean damage is plausible; usually the damage you see *at a lug* is improper torquing causing arcing, which can make a whole lot of heat. Some people think aluminum wire is more prone to this; I think it's all about setting the correct torque on the setscrew - and torque screwdrivers are now mandatory.
I don't know what's up with the bus bars (yellow things). It might just be weathering/age. However, if it was an overload, then the working theory is that *both* the lug *and* the bus bars overheated. Overheating that serious would require over 300A for quite some time. I don't think that would happen without a *rather memorable* event, like a dryer filling the house with smoke or something! And I would expect that event to utterly destroy the bus stabs on the branch circuit breaker, since those are only rated for 125A. Also, I would expect the panel to smell like the stench of burnt plastic.
On the other hand, the world keeps making better idiots. So I guess I could see it. Suppose the house has a heat pump with 140A of emergency heat. And/or someone decides to install a 120A on-demand water heater. And/or they get a Tesla with an 80A charger. Maybe they crammed so many loads in here they plain overloaded the panel.
This for sure, that looks like a *very full* panel, Given that it's completely full of GE Q-line double-stuffed breakers, I suspect it's a rather small panel as well, like maybe only 12- or 16-space.
It would be in your interests to get a rather much larger panel. This panel will continue to be a pain-point due to its small size and overstuffed-ness. Of course that need could also be solved by fitting a subpanel somewhere, so you don't need to replace *this* panel to solve the overstuff problem, you can just have another panel next to it or somewhere else to give you some space. I generally want to see 40-ish spaces per house, that don't require double-stuffing breakers like these half-width GE's. That's so you can fit what you want, and have room for full-space AFCI and GFCI breakers. You may not want those breaker types, but you sure want the option.
If you force the seller to replace the panel, they will fit the smallest panel they can possibly get. So I'm not a fan of asking sellers to fix stuff, because I want a better repair than obligatory tenant-grade work.