, sorry but aerating isn't so much an overseeding process as it's been made out to be, wherever there's not a core hole or a plug for seed to lie against then it's basically like doing nothing and just throwing down seed, which does work but not so great, need seed to soil contact.
Aerating helps reduce thatch (when soil cores left on surface melt it makes soil meet the thatch and it helps compost the thatch) but cool season grasses besides bluegrass and zoysia don't create excess thatch normally, and some thatch is good,
plus aerating helps get the most important fall fertilizing down to the roots along with water and air creates more robust drought a disease etc tolerant roots.
Aerating is good for lawns that are already good or for something like a pure zoysia lawn that hasn't been aerated or dethatched but many zoysia lawns seem to do fine since the 80-90s I doubt some these solid zoysia lawns I've seen have even been cored or thatched.
Coring you can also topdress compost afterwards to amend poor clay/sandy soil in an already-decent lawn it gets the compost deeper than just topdressing and doesn't ruin the lawn like tilling the whole thing while adding compost.
Slice seeding is what you want, and usually not dethatching, slicer is basically a sharper dethatcher that doesn't harm existing grass as much as a flail dethatcher (a tine dethacher is a gentler spring and doesn't really affect existing turf but is good for raking out thatch if there even is excess thatch), only need 1/4" deep grooves for grass to grow, and really bad areas with no turf can run it slow and deep and basically till the top few inches of soil (or also use a tiller there and get deeper) so it's a fluffy soil bed good for seeding. But grid pattern slice seeding will get you more grass to grow than any other method besides tilling the whole thing, a LIGHT topdress with some compost/good soil after the slicing will get even more to grow. Just topdressing with no slicing or coring also works well but slicing opens up the soil giving the roots an easier chance to get down there and establish.
I used to tine (not aggressive flail) dethatch, and then core aerate, and then slice seed and then broadcast seed but yes the aeration helps but besides that I don't think there's even a need to dethatch unless it's pure bluegrass or zoysia and even then it doesn't need thatching so often. The dead grass that a tine thatcher removes from most cool season lawns is mostly just dead discarded under blades, yes removing that helps get more seed to soil contact but depends on the soil type etc, if the soil not too sandy then even without dethatching, the slices are showing pure dirt for the seed to fall into and not falling into a blend of dead grass blades, and then it gets melted over once it's watered and gets good soil contact, and then the dead grass on top helps by holding moisture for germinating like putting straw over seeds or using blue coated seeds, and since it's dead grass already brown dead it won't possibly decompose over the tiny grass sprouts and kill them.