If 'm' as flag causes ^ and $ to gain magic as in

 m   Treat string as multiple lines.  That is, change "^" and "$" from
     matching the start or end of the string to matching the start or
     end of any line anywhere within the string.
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and $ matches end-of-line (or before newline) as in

It might be arguable that the newline would be matched by $ in

$ perl -Mre=debug -wle'"ABC\nDEF" =~ m/C(?:$)^D/m'
Freeing REx: `","'
Compiling REx `C(?:$)^D'
size 7 Got 60 bytes for offset annotations.
first at 1
rarest char D at 1
   1: EXACT <C>(3)
   3: MEOL(4)
   4: MBOL(5)
   5: EXACT <D>(7)
   7: END(0)
anchored "CD" at 0 (checking anchored) minlen 2
Offsets: [7]
        1[1] 0[0] 5[1] 7[1] 8[1] 0[0] 9[0]
Omitting $` $& $' support.

EXECUTING...

Guessing start of match, REx "C(?:$)^D" against "ABC
DEF"...
Did not find anchored substr "CD"...
Match rejected by optimizer
Freeing REx: `"C(?:$)^D"'
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I understand that it doesn't. Making the newline explicit as in tye's example does

$ perl -Mre=debug -wle'"ABC\nDEF" =~ m/C(?:$)$\?^D/m'
Freeing REx: `","'
Omitting $` $& $' support.

EXECUTING...

Compiling REx `C(?:$)
?^D'
size 11 Got 92 bytes for offset annotations.
first at 1
rarest char D at 0
rarest char C at 0
   1: EXACT <C>(3)
   3: MEOL(4)
   4: CURLY {0,1}(8)
   6:   EXACT <\n>(0)
   8: MBOL(9)
   9: EXACT <D>(11)
  11: END(0)
anchored "C"$ at 0 floating "D" at 1..2 (checking floating) minlen 2
Offsets: [11]
        1[1] 0[0] 5[1] 8[1] 0[0] 7[1] 0[0] 9[1] 10[1] 0[0] 11[0]
Guessing start of match, REx "C(?:$)
?^D" against "ABC
DEF"...
Found floating substr "D" at offset 4...
Found anchored substr "C"$ at offset 2...
Starting position does not contradict /^/m...
Guessed: match at offset 2
Matching REx "C(?:$)
?^D" against "C
DEF"
  Setting an EVAL scope, savestack=6
   2 <AB> <C
DEF>         |  1:  EXACT <C>
   3 <ABC> <
DEF>         |  3:  MEOL
   3 <ABC> <
DEF>         |  4:  CURLY {0,1}
                           EXACT <\n> can match 1 times out of 1...
  Setting an EVAL scope, savestack=6
   4 <ABC
> <DEF>         |  8:    MBOL
   4 <ABC
> <DEF>         |  9:    EXACT <D>
   5 <ABC
D> <EF>         | 11:    END
Match successful!
Freeing REx: `"C(?:$)\n?^D"'
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