Kingmakers controller support
Intended, but not marked. Kingmakers has no controller support of any kind listed on Steam, while the game director says gamepad support is intended and might not be working when Early Access launches. For a game that is not out, a blank Steam field means nobody has declared support yet; it does not mean support has been ruled out.
No controller support is marked on Steam, but the director says the studio intends gamepad support, possibly not in time for the Early Access launch. What would change this: the controller fields filled in on the Steam page, or a developer post saying pads work in a build.

What the Steam page records
Steam stores controller information as a set of yes-or-no fields that developers fill in. For Kingmakers every one of them is currently no:
The Epic Games Store page carries no controller information either. When a player opened a thread on the Steam forum about the missing controller label, the game director replied later; his answer is below.
What the developer has said about game pads
The direct answer came in that thread, which a player opened on seeing no controller support listed:
“We do intend gamepad support, ultimately Kingmakers will be ported to console(s). However, we might not yet have gamepad support working when EA launches.”
Three things are in that reply and nothing more: gamepad support is intended, the studio expects to bring the game to consoles eventually, and Early Access may launch without pads working. It names no console and no date; the console picture is on Kingmakers on consoles.
Before that, the subject had come up sideways. Explaining why the strategy interface was rebuilt, the game director said the old one did not suit pads:
“Also for game pads this system wasn’t going to work well.”
That shows controllers were a consideration when the interface was redesigned, and a later update on the same rework said “as a side benefit it will work better with gamepads”. The redesign itself is described on what Kingmakers Early Access includes.
Why it is a hard question for this game
Kingmakers is two games at once: a third-person shooter and a strategy layer where you place buildings and order troops from above, like the view pictured at the top of this page. That strategy layer is the part the director said was rebuilt partly because the old version did not suit pads. How the two views work is on Kingmakers gameplay explained.
If you play on Steam Deck
This matters most there. Steam Input can map keyboard and mouse controls to the Deck’s buttons and trackpads for any game, but that is not the same as the developer supporting a controller. The Deck answer is on Kingmakers on Steam Deck.