I think you should just do whatever feels right. People seem to be happy doing it either way, and get good results.
For me, I was borderline for qualifying for successful Periareolar surgery. I worked out and used creams and such to try to lose as much chest fat as possible to guarantee good results for myself. I know some people don't have a choice in what surgery they qualify for, but I've had a very rough life, and I'm very suicidal all the time without the problems of gender dysphoria. I honestly don't know if I could mentally handle having large scars across my chest if I don't need them. I couldn't lose much up top, and have been so anxious about surgery (I plan to have it in Feb/March).
However, I am just over a month on T now and (somehow) have actually been losing weight, not gaining, and my chest is getting significantly smaller now (I probably lost half a cup size in the past week). I'm going to continue trying to get it to shrink as much as possible, and it's slowly giving me more peace of mind about surgery outcomes. So for myself, I'm glad I got to start T first. At the same time, I'm also glad that I'm going to have saved up enough money for surgery just in time to get it done shortly after starting T. I have scoliosis and asthma and binding is a severe challenge for me, so I'm glad I'll be able to get surgery before or around the time my facial hair might start coming in/changes might start becoming more obvious.
I know all my reasoning may sound complex and over-thought, but this issue is a real big source of anxiety for me, and this feels like the best course of action for myself.
Good luck with whatever you choose to do, and congrats on being so close to finally starting this journey of change!