For their Data Science program, I believe a PhD is still a requirement, but it seems you have one. The bigger caveat is that it's not really a "bootcamp" per se, in that there are no real lessons or assignments. Applicants to the program are expected to be nearly ready for entry into the job market already. The program is rather for developing soft skills and networking. Although the program centers around a project, the project is really more of a conversation piece for interviews.
Pre-COVID, this program was free, which was one of the best things about it. Now I believe there is an ISA instead.
If you haven't worked as a Data Scientist before, have a portfolio of code I can look at.
If you have, I care about how relevant your experience is to my problems, not about where you learned pandas.
The value add from the name of a respected bootcamp isn't as high as you think.
Getting a job will come from your effort and creativity in the search process post-bootcamp.
Which program you choose depends on your time, money, and energy constraints. The good news is that there are plenty of options out there.
I wrote a post [1] outlining the constraint tradeoffs based off my experience in a bootcamp and subsequent career movement through the data world.
[1] https://www.dataindependent.com/blog/joining-data-bootcamp/
Edit: Emphasis on the 'name' of the bootcamp (vs the other value adds you earn)
You can probably do much better than you think.
Maybe a data engineer can chime in, but the market certainly seems better for that skillset than for us python, R, sql, stats people who are a dime a dozen.
First off, have you tried applying for DS jobs yet? What were the results? As others have alluded to, a bootcamp is not a mandatory prerequisite for a DS job, and is no substitute for on-the-job experience. If you're finding that you can generally get callbacks from recruiters/hiring managers based on the strength of your current resume (or have friends in the industry who can give you referrals), then you probably ought to just keep up with that approach. You can refine your resume and interviewing technique based on the parts of the interview process you struggle most with, and eventually the pseudorandom number generator that is interviewing will work out for you.
If you're submitting your resume to lots of companies and never hearing anything back, then a bootcamp might make sense. My general advice for a bootcamp is to look for one that meets your needs and has incentives aligned with yours. In general I think that is probably a better way to choose a bootcamp than trying to figure out which ones employers respect the most. There's no one right answer to that question, and honestly that answer can change over time: you can see in some of the other comments that it looks like the Insight fellowship has changed significantly in response to the pandemic, and I know that the bootcamp I did changed fairly substantially in the years after my cohort. IMO none of the existing bootcamps have the history or pedigree at this point for their name to mean a whole lot on its own.
Generally in my experience bootcamps tend to be split into two groups: 6-8 week project-based ones, mostly focused on polishing candidates that are already close to being ready to get DS jobs; and 3-6 month training-focused ones, designed to upskill people who have a minimum baseline set of skills but are not particularly close to being competitive DS candidates. If you have already been doing some reading on the side and mostly need an introduction to hiring companies (and maybe a project to talk about), shorter fellowships make more sense. If you think you need more training in core DS concepts, then a longer program may be better. Prefer programs that only make money when you get a job (either via as your recruiter or via an income share) versus programs that charge an upfront tuition, although note that the former tend to be harder to get into and may actually exclude you from some jobs immediately after graduation (if they work as your recruiters, large companies with their own recruiting arms may not be willing to pay the extra recruiter fees).
Finally, if you're in a bootcamp, make sure that you're doing something to differentiate you from your peers. The first time I saw a bootcamp candidate talk about their model to find ideal jogging routes based on RunKeeper data hosted in a Flask app using the Google Maps API it was super impressive; the third time I saw a candidate present this same basic project was much less so — it was obvious that to save time all the bootcamp participants had been taught the same basic stack and given a lot of hints for what kinds of projects they could do.