You could use the following:

[\p{QMark}`\N{U+275B}-\N{U+275E}\N{U+1F676}-\N{U+1F678}\N{U+2826}\N{28
+34}]
[download]

What follows explains how this was derived.

---

Let's start by collecting some info about each character.

for q in \" \' « » ‘ ’ ‛ “ ” ❝ ❞ 🙶 🙷 \`; do
   uniprops --all --single -- "$q" >"props-$q"
done

The programs uniprops and unichars (used later) are provided by Unicode::Tussle.

---

Let's collect what we have.

perl -e'
   use 5.014;
   use warnings;

   my %props; while (<>) { chomp; ++$props{$_}; }

   say "$props{$_} $_"
      for
         sort { $props{$b} <=> $props{$a} || $a cmp $b }
            keys(%props);
' props-*
[download]

The list is long, but a lot are redundant (aliases and short forms).

[It would be nice if we could tell it to output just one form of equivalent forms!]

---

We consult perluniprops and see that no interesting properly matches all 14. This is not surprising, since we have charcters from two General Categories.

9 Punctuation
5 Symbol
[download]

The 9 punctuation characters all match \p{Quotation_Mark} aka \p{QMark}! This is the full set of quotation marks:

$ unichars -au '\p{QMark}' | cat
‭ "  U+00022 QUOTATION MARK
‭ '  U+00027 APOSTROPHE
‭ «  U+000AB LEFT-POINTING DOUBLE ANGLE QUOTATION MARK
‭ »  U+000BB RIGHT-POINTING DOUBLE ANGLE QUOTATION MARK
‭ ‘  U+02018 LEFT SINGLE QUOTATION MARK
‭ ’  U+02019 RIGHT SINGLE QUOTATION MARK
‭ ‚  U+0201A SINGLE LOW-9 QUOTATION MARK
‭ ‛  U+0201B SINGLE HIGH-REVERSED-9 QUOTATION MARK
‭ “  U+0201C LEFT DOUBLE QUOTATION MARK
‭ ”  U+0201D RIGHT DOUBLE QUOTATION MARK
‭ „  U+0201E DOUBLE LOW-9 QUOTATION MARK
‭ ‟  U+0201F DOUBLE HIGH-REVERSED-9 QUOTATION MARK
‭ ‹  U+02039 SINGLE LEFT-POINTING ANGLE QUOTATION MARK
‭ ›  U+0203A SINGLE RIGHT-POINTING ANGLE QUOTATION MARK
‭ ⹂  U+02E42 DOUBLE LOW-REVERSED-9 QUOTATION MARK
‭ 「 U+0300C LEFT CORNER BRACKET
‭ 」 U+0300D RIGHT CORNER BRACKET
‭ 『 U+0300E LEFT WHITE CORNER BRACKET
‭ 』 U+0300F RIGHT WHITE CORNER BRACKET
‭ 〝 U+0301D REVERSED DOUBLE PRIME QUOTATION MARK
‭ 〞 U+0301E DOUBLE PRIME QUOTATION MARK
‭ 〟 U+0301F LOW DOUBLE PRIME QUOTATION MARK
‭ ﹁ U+0FE41 PRESENTATION FORM FOR VERTICAL LEFT CORNER BRACKET
‭ ﹂ U+0FE42 PRESENTATION FORM FOR VERTICAL RIGHT CORNER BRACKET
‭ ﹃ U+0FE43 PRESENTATION FORM FOR VERTICAL LEFT WHITE CORNER BRACKET
‭ ﹄ U+0FE44 PRESENTATION FORM FOR VERTICAL RIGHT WHITE CORNER BRACKET
‭ ＂ U+0FF02 FULLWIDTH QUOTATION MARK
‭ ＇ U+0FF07 FULLWIDTH APOSTROPHE
‭ ｢  U+0FF62 HALFWIDTH LEFT CORNER BRACKET
‭ ｣  U+0FF63 HALFWIDTH RIGHT CORNER BRACKET

The 5 symbol characters aren't in any useful category. The symbols are:

$ grep -L ^QMark$ props-* \
| perl -CS -ne'
   use 5.014;
   use warnings;
   use charnames qw( );

   s/^props-//;
   $_ = ord($_);
   printf "U+%05X %s\n", $_, charnames::viacode($_);
' \
| sort
U+00060 GRAVE ACCENT
U+0275D HEAVY DOUBLE TURNED COMMA QUOTATION MARK ORNAMENT
U+0275E HEAVY DOUBLE COMMA QUOTATION MARK ORNAMENT
U+1F676 SANS-SERIF HEAVY DOUBLE TURNED COMMA QUOTATION MARK ORNAMENT
U+1F677 SANS-SERIF HEAVY DOUBLE COMMA QUOTATION MARK ORNAMENT
[download]

So you could use

[\p{QMark}`\N{U+275D}\N{U+275E}\N{U+1F676}\N{U+1F677}]
[download]

---

Four of those you listed have "QUOTATION MARK" in their name, so why aren't they matched by \p{QMark}?

Well, they're actually "QUOTATION MARK ORNAMENT". U+275D, U+275E, U+1F676 and U+1F677 are all dingbats (emojis from before emojis was a word, kinda). They're not meant for use in text.

There are three more of these:

U+0275B HEAVY SINGLE TURNED COMMA QUOTATION MARK ORNAMENT
U+0275C HEAVY SINGLE COMMA QUOTATION MARK ORNAMENT
U+1F678 SANS-SERIF HEAVY LOW DOUBLE COMMA QUOTATION MARK ORNAMENT
[download]

---

Finally, this table also points out two braille characters you might want to include.

U+02826 BRAILLE PATTER DOTS-236
U+02834 BRAILLE PATTER DOTS-356
[download]

---

Update: Added the first section (the summary/"tl;dr") and the last section about why the 5 aren't quotation marks. Added the suggestion for additions to the list. Small wording tweaks.