I could not find any report of this issue in the GNU Bug Tracker or the
PROBLEMS file, but I apologize if maybe syntax highlighting errors do not
count as bugs.

That said, emacs on my machine at least seems to have an issue with
string literals in Bash. I have attached an image of the text below so
that the color can be represented. However, an example of faulty
highlighting in text is:

#!/bin/bash
partiallyquotedword=$'hello\''
echo "$partiallyquotedword"
partialword=$'hello\''
echo "$partialword"
echo sample text
echo hi\'
echo highlighting finished

The above will, from the escaped single quote in the second line,
be highlighted as a string until
the next single quote. That is, the final line of the provided example text
is correctly not treated as part of a string.

To be more concise, (my version of)
emacs does not seem to treat an
escaped single quote in a string literal as actually being escaped,
though this works in Bash.

(Build and system information below)

In GNU Emacs 27.2 (build 1, x86_64-pc-linux-gnu, GTK+ Version 3.24.27,
cairo version 1.17.4)
 of 2021-03-26 built on orion
System Description: Artix Linux

Recent messages:
For information about GNU Emacs and the GNU system, type C-h C-a.

Configured using:
 'configure --prefix=/usr --sysconfdir=/etc --libexecdir=/usr/lib
 --localstatedir=/var --with-x-toolkit=gtk3 --with-xft --with-wide-int
 --with-modules --with-cairo --with-harfbuzz 'CFLAGS=-march=x86-64
 -mtune=generic -O2 -pipe -fno-plt' CPPFLAGS=-D_FORTIFY_SOURCE=2
 LDFLAGS=-Wl,-O1,--sort-common,--as-needed,-z,relro,-z,now'

Configured features:
XPM JPEG TIFF GIF PNG RSVG CAIRO SOUND GPM DBUS GSETTINGS GLIB NOTIFY
INOTIFY ACL GNUTLS LIBXML2 FREETYPE HARFBUZZ M17N_FLT LIBOTF ZLIB
TOOLKIT_SCROLL_BARS GTK3 X11 XDBE XIM MODULES THREADS LIBSYSTEMD JSON
PDUMPER LCMS2 GMP

Important settings:
  value of $LC_MONETARY: en_US.UTF-8
  value of $LC_NUMERIC: en_US.UTF-8
  value of $LC_TIME: en_US.UTF-8
  value of $LANG: en_US.UTF-8
  value of $XMODIFIERS: @im=fcitx
  locale-coding-system: utf-8-unix

Major mode: Fundamental

Minor modes in effect:
  tooltip-mode: t
  global-eldoc-mode: t
  mouse-wheel-mode: t
  tool-bar-mode: t
  menu-bar-mode: t
  file-name-shadow-mode: t
  global-font-lock-mode: t
  auto-composition-mode: t
  auto-encryption-mode: t
  auto-compression-mode: t
  buffer-read-only: t
  line-number-mode: t
  transient-mark-mode: t

Load-path shadows:
None found.

Features:
(shadow sort mail-extr emacsbug message rmc puny dired dired-loaddefs
format-spec rfc822 mml easymenu mml-sec password-cache epa derived epg
epg-config gnus-util rmail rmail-loaddefs text-property-search time-date
subr-x seq mm-decode mm-bodies mm-encode mail-parse rfc2231 mailabbrev
gmm-utils mailheader cl-loaddefs cl-lib sendmail rfc2047 rfc2045
ietf-drums mm-util mail-prsvr mail-utils term/xterm xterm byte-opt gv
bytecomp byte-compile cconv tooltip eldoc electric uniquify ediff-hook
vc-hooks lisp-float-type mwheel term/x-win x-win term/common-win x-dnd
tool-bar dnd fontset image regexp-opt fringe tabulated-list replace
newcomment text-mode elisp-mode lisp-mode prog-mode register page
tab-bar menu-bar rfn-eshadow isearch timer select scroll-bar mouse
jit-lock font-lock syntax facemenu font-core term/tty-colors frame
minibuffer cl-generic cham georgian utf-8-lang misc-lang vietnamese
tibetan thai tai-viet lao korean japanese eucjp-ms cp51932 hebrew greek
romanian slovak czech european ethiopic indian cyrillic chinese
composite charscript charprop case-table epa-hook jka-cmpr-hook help
simple abbrev obarray cl-preloaded nadvice loaddefs button faces
cus-face macroexp files text-properties overlay sha1 md5 base64 format
env code-pages mule custom widget hashtable-print-readable backquote
threads dbusbind inotify lcms2 dynamic-setting system-font-setting
font-render-setting cairo move-toolbar gtk x-toolkit x multi-tty
make-network-process emacs)

Memory information:
((conses 16 49841 8635)
 (symbols 48 6117 1)
 (strings 32 15752 1794)
 (string-bytes 1 506502)
 (vectors 16 8128)
 (vector-slots 8 83328 7170)
 (floats 8 22 271)
 (intervals 56 191 0)
 (buffers 1000 12))