Long ago, a doctor in this forum wrote, that in most cases in overweight men there is most often a mixture of fat deposits and real breast tissue. And don't forget, that the belly fat contains much of the enzyme aromatase, which converts testosterone into estrogen. The fact, that your breasts don't change much, if you lose weight, is an indicator for gynecomastia. If you had only a lipomastia the breasts would shrink considerably too.
Agree with gotgyne's comments. I'm shaped I lot like you are - my chest is a mix of confirmed breast tissue, fat, and muscle.
I'm pretty sure the percentages have changed of that mix have changed as I've aged/meds/etc. Breast tissue can only really be confirmed by a mammogram or ultrasound here are a couple of things to check.
You may be able to feel firmer tissue over your pectorals as well as softer fat tissue. Another way to check (learned this recently) is to raise your arm over your head to stretch and flatten the pectoral; you may notice a conical outline that will be the breast tissue and fat.
You said you tried compression, it can definitely work for appearances, and some can provide some support. You might try a sports bra, and that may sound counter-intuitive (or even scary if you've never tried one), but it will provide better support for walking, and running especially without the compression around the lower lungs - and I find that sports bras actually make me look more fit and more like its muscle under that fat but have the same outline of a tank tee or compression tank (I'd still wear a non-tight black tee or hoodie if cool at least, and maybe a real tank too if you perspire a lot). I would guess XL/XXL in a stretchy sports bra (you don't need heavy compression to achieve a more-fit look just some modest shaping and lifting to back where pecs would be). I was better able to go on walks and jogs.
Good luck in what ever you do and especially being as healthy as possible.