It's not mysterious or confusing. The original definition is at https://agilemanifesto.org/
Similarly, everyone agrees that the Agile Manifesto is the OG source of Agile faith - and then everyone claims their own particular interpretation of it is the True Meaning anyway.
I've heard that one of the benefits of agile is identifying blockers and encouraging collaboration, but I saw much better results from assuming you've hired intelligent adults with work ethic and letting them reach out and collaborate as needed. Daily standups, sprints, boards, planning, etc. are great in a low-trust environment where you can't be sure people are doing the right things. But if you've hired self-directed people, that stuff just gets in the way.
I've known talented devs who are great people who still need more oversight than you describe. Usually they are ~5 years off from being full-trust, yet still valuable team members. Yes they benefit from daily standups.
I feel like there's this no true Scotsman thing going on with agile. Whenever someone describes their actual experiences with agile, there's always at least one person who speaks up and decries it as as not real agile and what agile should be.
At this point I don't care what agile should be. I just don't want management shoving agile down my throat anymore. I've yet to see it actually improve productivity for any team I've been on. Real agile must be exceedingly rare.