#JavaScript (ES6), 147 bytes

###Commented

JavaScript (ES6), 147 bytes

Commented

#JavaScript (ES6), 148 bytes

w=>F=(s,p=S=' ')=>(g=([c,...b],r='',x=c=='-')=>c?r[w-1]?c==S&&r+`
`+F(b):r[w+~x]?r+c+`
`+F(b):c==S?g(b,r+p)||g(b,r+p+c):g(b,x?r:r+c):r)(s)||F(s,p+S)

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#JavaScript (ES6), 147 bytes

w=>F=(s,p=S=' ')=>(g=([c,...b],o='',h=c=='-')=>c?o[w-1]?c==S&&o+`
`+F(b):o[w+~h]?o+c+`
`+F(b):c>S?g(b,h?o:o+c):g(b,o+p)||g(b,o+p+c):o)(s)||F(s,p+S)

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###Commented

w => // w = requested width
 F = ( // F is a recursive function taking:
 s, // s = either the input string (first iteration) or an
 // array of remaining characters (next iterations)
 p = // p = current space padding
 S = ' ' // S = space character
 ) => ( //
 g = ( // g is a recursive function taking:
 [c, // c = next character
 ...b], // b[] = array of remaining characters
 o = '', // o = output for the current line
 h = c == '-' // h = flag set if c is a hyphen
 ) => //
 c ? // if c is defined:
 o[w - 1] ? // if the line is full:
 c == S && // fail if c is not a space
 o + `\n` + F(b) // otherwise, append o + a linefeed and process the
 // next line
 : // else:
 o[w + ~h] ? // if this is the last character and c is a hyphen:
 o + c + `\n` + F(b) // append o + c + a linefeed and process the next
 // line
 : // else, we process the next character:
 c > S ? // if c is not a space:
 g(b, h ? o : o + c) // append c if it's not a hyphen
 : // else:
 g(b, o + p) || // append either the current space padding
 g(b, o + p + c) // or the current padding and one extra space
 : // else:
 o // success: return o
 )(s) // initial call to g() with s
 || F(s, p + S) // in case of failure, try again with a larger padding