Tokenize a Stack-Based language
Retina, 68 64 63 bytes

M!s`"(\\.|[^"])*"?|'.|\d+|\S
ms`^'(.)|^"(([^\\"]|\\.)*$)
"$1$2"


or

s`\s*((")(\\.|[^"])*(?&lt;-2&gt;")?|'.|\d+|.)\s*
$1$2¶
\ms`^'(.)
"$1"


I think this covers all the funky edge cases, even those not covered by the test cases in the challenge.

Try it online!