Mesh networks are relatively new to the Standard. True LE 5 SoCs should have what you need to get started.
I'm not sure how it works now, but especially for newer stuff I wouldn't rely on the fact that the hardware claims to support something -- if the software isn't there, it just doesn't really mean much.
But you are probably correct about the latest chips.
Many chip vendors have BT mesh implementations, including Nordic, TI, SiLabs, Cypress, Dialog, and ST.
I can't remember the exact details but I remember being disappointed when it was announced and I looked into it.
It does seem like there’s a lot of momentum in the BT-SIG to grow the standard over a long period of time, and there also are a lot of active contributors, so I do expect it to mature in the future.