Desmos 3D, 19 (+ \$\log_{256}(7\times2)\approx 0.475919\$) bytes

n=0
a=hsv(n,x,z
y=0

Input into \$n\$. Requires you to set the colour of the equation \$y=0\$ to the defined custom colour, as well as tick the Extend to 3D option, for an extra \$\log_{256}(7\times2)\approx 0.475919\$ bytes. The square is defined by \$0\leq x\leq 1,0\leq z\leq 1\$.

Try it here!

R, 74 bytes

\(h)image(matrix(1:1e6,1e3),c=outer(j<-0:999/999,j,hsv,h=h/360),ax=F,as=1)

Try it at rdrr.io

R, 98 bytes

\(n)image(matrix(seq(m<-outer(k<-0:255/255,k,Vectorize(\(a,b)hsv(n/360,a,b)))),256),c=m,ax=F,as=1)

Draw it on rdrr.io!
check byte count

Wolfram Language (Mathematica), 48 bytes

Image@Table[Hue[2#/a,j/a,1-i/a],{i,a=6!},{j,a}]&

Creates a 720x720 image using the Hue[h,s,b] builtin that expects its arguments (hue, saturation, and brightness in that order) normalized from 0 to 1. Some good fortune that 6!=720 is both shorter to code than 256 and also twice the 360 needed to normalize the hue argument. (Although I guess replacing 6! by 360 removes the need for the 2 and so yields the same code length.)

JavaScript (ES6), 190 bytes

Generates a <canvas> of 256×256 pixels and fills it by converting from HSV to HSL. Most probably not the shortest approach.

h=>{for(i=!document.write`<canvas id=c height=256>`<<16;i--;a.fillRect(x=i%256,y=i>>8,1,1,a.fillStyle=`hsl(${h} ${v=1-y/255,v-=l=v-v*x/510,v/(l<.5?l:1-l)*100} ${l*100})`))a=c.getContext`2d`}

(Don't) Try it online!

Graphical output

f=
h=>{for(i=!document.write`<canvas id=c height=256>`<<16;i--;a.fillRect(x=i%256,y=i>>8,1,1,a.fillStyle=`hsl(${h} ${v=1-y/255,v-=l=v-v*x/510,v/(l<.5?l:1-l)*100} ${l*100})`))a=c.getContext`2d`}

document.write = _ => undefined; f(123)

<div style="float:left"><input type="range" min="0" max="360" value="123" style="writing-mode:vertical-lr;direction:rtl" oninput="f(this.value)" /></div><canvas id=c height=256>

Scratch, 258 247 246 bytes

Somewhat optimal? Uses a square of side 320 px.

Try it here

define x(i
go to x:(-99)y:(-180
set pen(color v)to((i)/(3.6
set pen(brightness v)to(
repeat(320
set pen(saturation v)to(
repeat(320
pen down
pen up
[saturation
move(1)steps
end
set x to(-99
change y by(1
[brightness
define(c
change pen(c)by(.3125

For a bit of interactivity I customized it so that moving the cursor will redraw a new square, taking the x-coordinate of the cursor as the input. Here is an example output:

_{fun fact: before the previous edit, I was working with a version that named both custom blocks the empty block with an input. Now my Scratch project has an x () block whose input a reporter can be dragged into, but no text/number can be typed :o}

CSS, 102 83 bytes

div{--h:123;width:256px;height:256px;
background:linear-gradient(#000,#0000),linear-gradient(90deg,#fff,hwb(var(--h)0 0))
}

<div id=o></div><input type=number value=123 min=0 max=359 oninput=o.style.setProperty("--h",this.value);

The work is done by the second line of CSS in the snippet; the rest of the CSS makes the image visible and gives the input a default value for convenience; the HTML allows you to change the input's value. (Since CSS can't read input in any other way, I assume using a variable is legal.)

Edit: Saved 19 bytes thanks to @MatthewJensen.

Uiua 0.19.0, 24 bytes ^SBCS

°hsv⊞(⇌⊂⊂)⊸⇌÷⟜⇡₀256×η/90

Try on Uiua Pad!

Takes a hue angle in degrees on the stack and returns an image.

°hsv⊞(⇌⊂⊂)⊸⇌÷⟜⇡₀256×η/90
                      ×η/90 # convert to radians
              ÷⟜⇡₀256       # range 0...256 divided by 256
           ⊸⇌               # make a reversed copy of the array
    ⊞(⇌⊂⊂)                 # make a table of all 257x257x1 combinations
°hsv                        # HSV -> RGB
                            # outputs as image since shape is [257 257 3]