Term for a doorway without a door

Solution 1:

Doorway would indeed be acceptable. Consider that, if the doorway has a door, you cannot see through to the other side unless the door is open. In this case, depending on your angle and the location of the door, it is perfectly possible that the door is entirely invisible. If so, its existence or non-existence is irrelevant to your perception of the doorway (or frame). So doorway is applicable regardless of the existence of a door.

Solution 2:

If it's curved it's an archway.

If it's entirely right angles it's a trabeation.

trabeated: designed or constructed with horizontal beams or lintels –MW

Credit to The Sims 4, calling some of them post-and-lintel entry frames and describing one as trabeated.

Solution 3:

You might consider entryway and entranceway.

entryway

A passage for affording entrance.

Word Origin: (1740-1750); Americanism; entry + way

Random House

Peeking his head through the entryway, he saw a tiny figure hunched over a lathe in the dark interior of the room. The Temple of thé Wild Geese

This is an odd type of room—no windows at all—and no door in the entranceway—There must be a door. How did I get in here? Tumbleweeds: An Authentic Collection of Windblown Tales of Americana Caught in the Cross Hair

There's no door in the entryway to the structure, and you suddenly understand that one is not necessary. What Lies Beneath the Clock Tower

Google Books