I worked as a lab tech in a PB production facility for 3 years. AMA

I'll start with some fun facts:

1. If the "natural peanut butter contains anything other than peanuts, salt, and sugar, it's not natural. Most "Natural No Stir" are like this. They use Palm oil as a stabilizer to keep the peanut oil from separating. You know how Palm oil is produced? They pay poor, impoverished people from 3rd world countries to clear-cut palm forests with no ability to properly replant the trees. They then grind these trees into pulp and basically"squeeze" out the liquids then separate the oil. It's then modified to actually be the stabilizer so it's not even in its natural state. The literal CEO of skippy came out and said most natural PB is a sham. Also peanut butter with palm oil tastes gross imo. First time I had it it gave me the shits fuck you JIF natural.

2. A large number of PB off brands with generic names like "simply good" and pure goodness" or whatever combination of two positive adjectives they use, are almost all the same or very similar formulas. The company I worked for was designed in a way that allowed them to change formulas on the fly and make just about any kind of PB they needed. They supplied most off brands out there including Meijer, Kroger, and Great Value. I will say, as much I hate to admit it, of all the off brands Great Value is the best. They have their own dedicated formula just like the name brands and it actually tastes good. Meijer and kroger taste like shit because they use a bland formula that uses more stabilizer.

3. What keeps the oil from separating like what OP has is the stabilizer. Imagine how gelatin powder make jello. In a way that's how the stabilizer works. When it's added at high temps it liquifys and mixes in with the oil and ground peanuts and holds everything in place. Then upon cooling it "sets." One test we actually do is test the set of the PB and we have machines that tell us just how hard the set is. There are no natural stabilizers, see my palm oil rant above. If you want a truly natural PB it's going to have ground peanuts, peanut oil, salt, and a little sugar. It will separate. I actually prefer it like this as I take a bag of mixed nuts, crush them up real good, and mix them with the natural PB to make a super crunch mixed nuts butter and it's amazing. Since so much extra solid matter has been added it actually helps prevent further separation.

4. You can tell, between to different PB formulas, which has more stabilizer by looking at it and tasting it. More stabilizer causes a waxy/plasticy look to the top of the PB when it sets. If one has a glossier/wet shine it it and the other a kind of shinny, waxy, look then the glossier one more than likely used less stabilizer. When you go to scoop it out if is rather solid and there's no sag in the butter, that's a good amount of stabilizer. If you eat them and one causes you to feel more stickiness in your mouth than the other than that one has less stabilizer. Peanut butter without stabilizer will stick to your mouth a lot more than stabilized butter.

5. Stabilizer will make the PB more bland. Feel like testing this? Get Meijer PB. It has a fuck load of stabilizer in it. It's super hard, super waxy looking and bland as fuck. It's almost not even peanut colored.

6. There are two main peanuts used in the industry. There's actually many kinds but two most common. "Jumbo runners" and "#1 runners." Jumbo's are your top tier nuts, they are big and flavorful. We had to sample the peanuts and taste test them. We were supposed to get a single cup and roast them and then taste them. When we did this with jimbo's we'd do several cups and snack on them all day. They are delicious. Our company made a lot of skippy as their plants couldn't manufacture it all and it was easier to contract it out to us. Skippy uses exclusively jumbos and pre tests and approved of shipments for us. We still do our own in house but it's not necessary. Then there's the #1s. These are little nuts that don't pack as much natural flavor like the big bois. Because of this they are roasted to higher temps to bring out and add flavor. Look at the color of skippy butter vs great value butter. GV is super dark butter why? Because it uses almost exclusively #1s. Bit it still actually tastes good why? Because they roast the shit out of this nuts and that dark roasting add a bunch of flavors they don't get as much in the jumbos.

There's probably more I could go on about but I've been tapping away at my phone long enough.