Knight-fill a grid

Octave, 73 bytes

function a=F(s,a)do;b=a;until(a=~s&imdilate(a,de2bi(")0#0)"-31)))==b;a+=s

Online Demo!

*Some changes applied to run in rextester.

A function that takes a 2d array of 0 & 2 as wall and an array of 0 & 1 as initial location and outputs an array of 0 & 1 & 2.

JavaScript (ES6), 116 bytes

f=(s,l=s.search`
`,t=s.replace(eval(`/(x| )([^]{${l-2}}(....)?|[^]{${l+l}}(..)?)(?!\\1)[x ]/`),'x$2x'))=>s==t?s:f(t)

v=(s,l=s.search`
`)=>!/^(#+)\n\1\n[^]*x[^]*\n\1\n\1$/.test(s)|s.split`
`.some(s=>s.length-l|!/^##.+##$/.test(s))&&`Invalid Input`

textarea{font-family:monospace}

<textarea rows=11 cols=33 oninput=o.value=v(this.value)||f(this.value)></textarea><textarea rows=11 cols=33 id=o reaodnly></textarea>

Based on my answer to Detect Failing Castles. Fills using xs.

Python 3, 394 387 381 356 352 347 319 313 154139 bytes

• 154 bytes after only counting the core function and not the function concerning I/O formatting
• saved 7 bytes: thanks to @Jacoblaw and @Mr.Xcoder: except:0
• saved 28 bytes!!!: Thanks to @ovs: got rid of try: except block and several other golf
• Thanks to @Dave for the beautiful test module.
• saved 6 bytes: g[(a,b)] as just g[a,b]
• @nore saved 15 bytes!!!:

def x(g,a,b,m):
 if(a,b)in g and"!">g[a,b]or m:
  g[a,b]="@"
  for i in 1,2,-1,-2:
   for j in 3-abs(i),abs(i)-3:g=x(g,a+i,b+j,0)
 return g

Try it online!