Some good information here, other information I cannot agree with. As a guy who's intimately familiar with the topic I thought I'd weigh in and lay out what I strongly believe to the best way to know the problem and tackle it.
Skinny-fat is looked upon in the fitness community as a 'special' condition that requires a 'special' method to combat it ("Only eat clean foods from now on!"). This is not true, it is nothing special, and the mechanics behind building muscle and losing fat are simple and remain the same for all people, skinny-fat or not.
What skinny-fat is, is simply the short end of the stick in terms of body genetics. It is poor genetics, hormones, and structure, which lead to a certain Worst of Both Worlds: 1) a tiny 'ecto' frame, PLUS, 2) a massive depositing of fat all over it.
The website Skinny Fat Transformation does well to demonstrate this root of the problem. However, paradoxically, the site still takes the 'special method' route in dealing with it, and in line with this, the owner's sudden ascension to a 'normal' or 'super-normal' progression, when the whole point is that he's sub-normal, makes me think he's on TRT. But it's a business after all.
TRT is a legitimate cure and will shave off years of a painful body recompositioning journey. But if you're gonna go the natty route here's what I suggest:
1. Set aside conventional bodybuilding advice. With your genetic profile it doesn't apply to you. Most of it is written by gifted & juicing bodybuilders and powerlifters.
"Bulking" will turn you from skinny-fat to morbidly obese with your poor metabolism and partitioning.
"Recompositioning" is not an option because of your poor hormones. If they were good enough to allow it, then your body wouldn't be resting in a skinny-fat state in the first place. Even if hypothetically you could, it would still be way too slow compared to straight up fat loss.
"Cutting slowly" won't work because your basal metabolic rate will naturally be very low.
"Going hard" in the gym with a vast array of exercises will be a waste of time, as initially you're gonna be cutting (see below) and your body won't even be anabolic to make good on your efforts.
2. Get a DEXA Scan. This is of FUNDAMENTAL IMPORTANCE. An absolute MUST. Drive far and away to do it. Pay for a hotel in the big city where scans are done if you have to. A scan in my city costs $125, but the information it gave me was so illuminating upon hearing it that I would have paid a grand to know it.
A DEXA scan, for those who don't know, is a low-intensity x-ray that determines body composition (lean mass vs. body fat) accurately in a way that calipers or visual inspection cannot. As a skinny-fat, the results thereof will be depressing. The scan will show that your body fat percentage vs. lean mass ratio is significantly worse than even your most unflattering estimates. It will show that you don't have a normal frame, but that you all along you've had a small frame underneath an illusion of fat. It will show that in order to get normally lean you will have to lose a huge amount of bodyweight and become very, very 'skinny'. All depressing, but also uplifting, because now you know for sure what you have to do.
3. Diet AGGRESSIVELY to a low bodyweight. Stay on a calorie restricted diet for as much as 6 months to shed bodyweight and reveal your underlying frame. Make the diet meat-focused for satiety/fullness and for the protein. Add in regular cardio to rack up higher deficits. Again, don't listen to thick-framed juicers talking about "cutting slowly". They can say "I'm cutting at 2700 cals brah!". That's their world. With your metabolism you may have to go sub-1500. This will be a period of severe mental hardship.
4. Do calisthenics. The purpose of lifting weights during a calorie deficit is to preserve muscle mass. The purpose of doing calisthenics here rather than barbell work is that it's simply more time-efficient. Jumping on a dip bar and cranking out some reps is just a lot easier than going through the motions of loading up a barbell and getting spotted for some intense reps on the bench. You have barely any muscle in the first place, and it's not gonna go up much while you're dieting, so better to just mentally and time-wise do the bare minimum to preserve what little you have now. One added benefit of calisthenics is that your reps will go up as you lose weight.
5. Once you're gotten to a level of leanness you're satisfied with, maintain or eat very slightly above maintenance for years and very slowly pack on mass. Never "bulk". The take-away here is that as a skinny-fat "The Diet" never really ends. Your body, your natural appetite, and your metabolism/hormones, want you to be a skinny-fat. To prevent a return to this you need to maintain the constant vigilance of a diet even though you're not actually on one anymore calorie-wise. This is where eating "clean" works.
Here are 2 strong examples of exactly I'm talking about. First guy,
probably normal BMI, normal arms, but conspicuously puffy belly. Leans out and
a tiny frame is revealed.
Second guy, Indian, is somehow simultaneously 45% body fat yet has twig arms and tiny wrists. Loses a quarter of his bodyweight yet is still kind of fluffy.
Hope this helps. It would have helped me immensely starting out. Skinny-fats are often chided for a lack of effort based on a lack of results, but behind the scenes we are the ones who have to work the hardest.