E dealer, nobody vulnerable. This was a typical auction, 3NT usually means 25-26. Nobody bid the slam, yet the hands offer excellent play for 6NT, with a possible 12th trick in ♦ or ♠. I'd probably start by testing if South has the ♦K then try to get info on the ♠ distribution, maybe there's a more sophisticated squeeze or throw-in play which offers better probabilities. Thoughts on that appreciated but I want to focus on the bidding really.
I think slam *should* be bid on these cards, but I'm not sure *how* to bid it. If both players bid their cards literally according to SAYC or most other systems, they'll end up underbidding it. 4NT (whatever form of Blackwood) is no use, but there's no easy way to enquire about kings without committing to 6NT.