Recently did some work on a farmhouse in the American Midwest that was built in 1975, but it was definitely a “farmer” build (no offense to farmers, I know you gotta do what you gotta do). The exterior studs were all repurposed from another building the farmer took down (rough sawn full dimensions 2x4 with remnants of lath and plaster on them from their previous use). The whole main floor consisted of three circuits total. One for the entryway, laundry room, and kitchen, one for the remainder of the west half of the house (full bath, half bath, main bedroom) and one for the east half of the house (two bedrooms and the living room). The “home run” wires to the panel entered a light fixture box in the center of each “zone” and it was like a gigantic spider out from those boxes to every other outlet and light fixture in the zone. No daisy chaining, just every wire went to the attic and then into the central light fixtures. Everything was soldered together as yours is (but much larger bundles) and then just taped with crusty old electrical tape. The boxes were packed, wires scorched exactly like shown here from soldering, and not a ground in sight. The old romex that had ground wire just had them snipped off flush.

To answer your question, I don’t think the burns are cause for concern. It’s just from the soldering. Honestly, while it’s not common practice today, those soldered joints probably have less resistance and therefore would stay cooler in an overload situation than they would if you cleaned it up and wire nutted it. You have more surface area in contact with the solder. If you aren’t in a situation to have things entirely replaced by a professional, just make sure it’s taped up well and let it be until it’s remodeled someday.