Hello and welcome,
@PK2026 !
Sagging breasts are caused by gravity (unless you plan on moving to the ISS there's no getting away from that!) and the natural aging process: the skin and ligaments that support our breasts stretch out and lose elasticity over time. Strengthening back and core muscles can help improve posture, and strengthening chest muscles can help the whole chest area look more lifted in general. So yes: it's certainly possible doing those things will affect your physique in ways you desire. I think the larger benefit, however, is that, if you do the work, you will be stronger, and you will gain confidence in knowing that this increased strength is something you accomplished through your own efforts. Possibly it will also help you to focus more on things you can control (choosing to do work to get stronger) versus things you cannot (gravity, genetics).
Re: weight loss: I don't think it will reduce existing sagging. It might slow further sagging. But weight fluctuations exacerbate loss of elasticity. So if you want to go that route, I would definitely recommend taking it slowly and making changes which you are confident will be sustainable for you.
I cannot speak to whether or not guys "care about this issue". Presumably the answer to that depends on the guy. (I'm 55 and female. But I've never wanted to date guys, have expended rather a lot of energy over the years trying to dissuade various guys from their attempts to pursue me in that fashion, and have never cared about the opinions of people who judge other people based on their physical appearance.)
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