ASK NC

Mostly Linux environment (plus 1 Windows 10 box), 2.5-10GB networking, currently using rsync for backup to naked 14TB disk in WeMe "toaster" adapter (USB).

What would best NAS box to support this environment?

I would go for DS220+. Their active backup for business is like nothing else in the market.
Otherwise, with RSYNC you can use any NAS.