The core is really adaptive planning and acceptance/flexibility to uncertainty, biasing towards shipping first. There is no requirement to be spending all day in endless meetings, nor an opposition to documentation. If more documentation increases velocity, why would that be anti-agile?
More importantly, what works for you does not discredit another team's agile approach. I lead large and growing teams rapidly releasing greenfield software. We are definitively agile, and documentation is empirically key to that process. Perhaps your experience differs. I don't discredit that, merely provide my experience in contrast.
Waterfall's issue was that it stipulated there shalt be process from stage 1 before anyone even understands WTF anyone is doing. FrAgile(TM) is notorious for just cutting people loose and winging it, with no regard to system design, architecture and maintaining a cohesive whole over the entire process that keeps your business functioning.
You can't just NOT make SOP's you can't have an onboarding process that can't ne negotiated by the average person. Doing so is a recipe for burnout/churnout and failure.
"Working software over comprehensive documentation" is one of only 4 values of the Agile Manifesto, and it's in direct conflict with what you're calling Agile.