Targum Yonatan (TY) of Isaiah 52:13 identifies the servant as the anointed one:
הָא יַצְלַח עַבְדִי מְשִׁיחָא יְרוּם וְיִסְגֵי וְיִתְקוֹף לַחֲדָא (source)
Behold, my servant the Messiah shall prosper, He shall be exalted and extolled, and He shall be very strong. (source)
TY of Isaiah 53:3 describes his appearance:
בְּכֵן יְהֵי לְבוּסְרָן וְיִפְסִיק יְקָר כָּל מַלְכְּוָתָא יְהוֹן חֲלָשִׁין וְדָוָן הָא כֶּאֱנַשׁ כֵּיבִין וּמְזוּמַן לְמַרְעִין וּכְמָא דַהֲוַת מְסַלְקָא אַפֵּי שְׁכִנְתָּא מִנָנָא בְסִירִין וְלָא חֲשִׁיבִין (source)
His visage shall not be the visage of a common person, neither His fear the fear of a plebeian; but a holy brightness shall be His brightness, that everyone who seeth Him shall contemplate Him. (source)
Between these verses is 52:14, which, in the MT, reads,
כַּאֲשֶׁ֨ר שָׁמְמ֤וּ עָלֶ֙יךָ֙ רַבִּ֔ים כֵּן־מִשְׁחַ֥ת מֵאִ֖ישׁ מַרְאֵ֑הוּ וְתֹאֲר֖וֹ מִבְּנֵ֥י אָדָֽם (source)
Just as the many were appalled at him — So marred was his appearance, unlike that of man, His form, beyond human semblance (source)
Here in the MT Hebrew the servant's appearance/visage is described as מִשְׁחַת, typically translated as 'marred' or similar. The same translation is given in the online version of the Qumran Isaiah scroll. The Septuagint version has ἀδοξήσει, translated here as 'despised'.
Given the context provided by TY, should we use the Qumran version, משחתי, and read "MAShAḤTI" = "I anointed" rather than "MIShḤAT" = "was marred"? Then 52:14 would read,
Just as the many were appalled [or amazed?] at him — So I anointed his appearance, unlike that of man, His form, beyond human semblance
and the sense would be "anointed (as in TY of 52:13) so that his appearance was made glorious beyond human appearance (as in TY of 53:3)".
(As a small additional point, this article points out that Isaiah 52:14 is the only instance of 'marred' in the Tanakh; but magicker72 points out that other forms of the verb do appear elsewhere.)
This question is prompted by reading Margaret Barker's book, Temple Mysticism - An Introduction (ISBN-13: 978-0281056347).
Edit 1: I removed references to Christianity, in the hope that that makes the question less likely to be closed as off-topic. I also added Targum locations.
Edit 2: I removed the long quote from Barker that made up the bulk of the original question, and now cite primary sources directly, in order to deemphasise the link to Barker, in the the hope that that makes the question less likely to be closed as off-topic.
Caveat and acknowledgement
I don't read Hebrew or Aramaic and haven't read TY extensively. I'm relying on copy-and-paste to quote Hebrew script, and I'm unlikely to spot any mistakes I make in copying. Thanks to magicker72 for giving an erudite answer, which I've used to improve the question.