Founder here, and this was the exact thing that stressed me out most too, so I get it. The straight answer first, then the why.
Rough shape most men are given: gentle walking from day one or two, desk and light work at around 1 to 2 weeks, and strenuous training including the gym held off until around 4 to 6 weeks, cleared by the surgeon following you up rather than by a date you pick yourself. The order Ben and Danny describe is right: lower body and light cardio come back before upper body, and direct chest work (bench, dips, flyes, heavy overhead) is the very last thing, because it loads the operated area most and in the window a bleed is most likely.
On the vest myth, they are correct to bin it. The vest is closing the space so fluid and blood cannot collect, that is all. Training in it does not protect you; the risk from early lifting is a haematoma, a blood collection reported at roughly 5.8 percent, and disturbing the tissue before it has settled onto the new contour. A big blood pressure spike from a heavy set is one of the recognised triggers, which is why even straining under squats gets held longer than people expect. I pushed a bit of cable work at three weeks, felt clever, and had a tighter more swollen chest the next morning as a plain telling off. Lesson learned cheaply, thankfully.
Two ranges worth holding in your head: bruising and swelling are usually worst in the first 2 to 3 weeks then ease, and the chest goes on settling for roughly 3 to 6 months, long after you are back training. There is a full breakdown in the exercise after gynaecomastia surgery guide and the week-by-week recovery piece.
The one thing I will flag hard: a side that suddenly swells tight and hard, especially in the first day or two, a fever, or a wound that opens or weeps, is a same-day call to your surgeon, not a post here and not something to train through. Your case depends on your grade and whether skin was removed, so the timeline your surgeon writes for you beats all of ours.