Fair point.
First off, the Peace Corps budget is tiny compared to most other federal agencies, at around $430 million a year right now. When I was serving, we liked to tell people that the US Army Band had a budget the size of our entire country program, which supported 120 volunteers and employed dozens of local staff members. Many of whom had advanced degrees and managed the American volunteers. I only got $4 a day because living at a local level is part of the job description. So it's not salaries overseas that drive the budget. Maybe the DC ones, if anything. It was simply too small to get DOGEd, and DOGE fell apart before they got down to the smaller agencies.
Second, yes, it's absolutely a form of soft power. That's a very up front, stated goal - the stated 3 goals are 1) Do development work as requested by the host country (formerly towards a goal of world peace and friendship), 2) be Americans overseas and talk about being an American, and 3) come back to the US and tell Americans about what you did and saw and experienced. So Goal 2 is literally to be present, and be you. There are some real rules, like don't attend local protests or actively campaign regarding US elections (per the Hatch Act, which applies to federal employees and members of the military as well), and a few others that make sense. At no point was I, or any volunteer ever told to pass along USG talking points. Most of us spent a lot of time shit-talking W, so if it's some grand conspiracy for that, they forgot to tell me and nearly everyone else I served with. It's often a bunch of crunchy granola super liberal people in the first place, and what few conservatives make their way in, often see real life and turn pretty lefty and activist-oriented afterwards.
And all of this wasn't even Kennedy's idea. The UK's VSO proved the point that there was demand for something like that in the US, and Kennedy took the idea (willingly) from university students during his campaign and ran with it.
It's worth also knowing that Peace Corps programs are only in countries that ask for them. They take years of work to identify sectors of work and which government ministries to work with, etc. before anyone ever gets on a plane. Communities are asked, and often go out of their way to request volunteers work with them. Some gringo doesn't just show up one day demanding things. Every single day I was working with people on things they wanted to do. The community where I lived tasked me with things, and I would try and find info for them and get something going. If I found promising ideas, I would bring them back and ask people what they thought. We did a whole village-wide assessment of potential projects, because without community buy-in, most ideas fall apart quickly.
I know you really wanted to shit on this for no reason other than lack of knowledge about it. Not that it's above criticism. There's things to fix or modernize. Funding projects is still a massive pain, and worse now. But name one thing that's perfect anywhere, though, right? If anyone thought it was perfect, that's a red flag all on its own.