What New Who episode feels the most like Classic Who?
I'd say Eaters of the Light personally.
There's something about the atmosphere of that episode. It's quiet, takes place mostly in empty British moorland. You've got some old folklore, there's nothing particularly high budget about it. You've got your classic get captured, misunderstanding, and escape through silly popcorn trick.
All it needs is to be a two parter, the length of a classic four parter. and there'd be plenty of room to add more misunderstandings, a few more capture and escapes, and more moments of just sitting and having a chat.
It gives me real Stones of Blood or the Daemons vibes. It's appropriate since the writer also wrote the Classic Who episode Survival way back when.