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In Wikipedia there is an article on Forensic linguistics that notes:

Forensic linguistics includes attempts to identify whether a person produced a given text by comparing the style of the text with the idiolect of the individual in question. The forensic linguist may conclude that the text is consistent with the individual, rule out the individual as the author, or deem the comparison inconclusive.

In 1995 Max Appedole relied in part on an analysis of Rafael Sebastián Guillén Vicente's writing style to identify him as Subcomandante Marcos, a leader of the Zapatista movement. Although the Mexican government regarded Subcomandante Marcos as a dangerous guerilla, Appedole convinced the government that Guillén was a pacifist. Appedole's analysis is considered an early success in the application of forensic linguistics to criminal profiling in law enforcement.

In 1998 Ted Kaczynski was identified as the "Unabomber" by means of forensic linguistics. The FBI and Attorney General Janet Reno pushed for the publication of an essay of Kaczynski's, which led to a tip-off from Kaczynski's brother, who recognized the writing style, his idiolect.

In 1978 four men were accused and convicted of murdering Carl Bridgewater. No forensic linguistics was involved in their case at the time. Today, forensic linguistics reflects that the idiolect used in the interview of one of the men was very similar to that man's reported statement. Since idiolects are unique to an individual, forensic linguistics reflects that it is very unlikely that one of these files was not created by using the other.

This appears to be very similar to the field of computational linguistics, in that at least in one case, it is being applied to questions of authorship. See here.

What is a general survey of Biblical scholars on the use of forensic linguistics in determining questions related to authorship of certain books in the commonly accepted New Testament canon? Are there examples of it being used to make a case for a "canon within a canon" by eliminating fraudulent letters (i.e. pseudepigrapha) existing in the commonly accepted canon?

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    I do not know how they might be analyzing the language, but with computers it is much easier to look for all sorts of things: congruities, variances, anomalies, distinctiveness (of various forms), etc. I used computer-analysis tools to consider the language of 1 and 2 Peter in the answer that I provided to your question regarding the authorship of 2 Peter.
    – Biblasia
    Oct 19, 2022 at 3:30
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    Good thoughts! An analysis of a typical pastor's set of sermons and/or letters might be a good way to objectively test and confirm one's technique. Some have tried to do linguistic computational analysis on secular literature using an algorithm for authorship verification. For example, see this report on the works of Shakespeare. aclanthology.org/D13-1151.pdf –
    – Jess
    Oct 19, 2022 at 16:20

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In terms of the NT Canon this question relates primarily to the issue of which letters attributed to Paul are truly Pauline. (For works that do not have recognized comparables, the issue is largely confined to anachronisms and cultural inconsistencies.) The basic methodology of identifying a mistaken attribution of a letter as Pauline using linguistics involves comparing the acknowledged Pauline corpus with a particular disputed letter. Beyond that, it gets very technical. According to an article in the Tyndale Bulletin 2018:

In terms of vocabulary, scholars usually point to five major idiosyncrasies: (1) hapax legomena {terms used only once}, (2) lexical richness, (3) missing indeclinables, (4)compound words, and (5) semantic deviations, including Grecisms and un-Paulinisms. Hapax legomena , lexical richness, and missing indeclinables seem to be the most important lexical anomalies for exegetes. In terms of syntax, scholars usually point to four major peculiarities: (1) interclausal relations, (2) structural irregularities in terms of anacolutha, parentheses, and ellipses, (3) miscellaneous uses of ὡς, articles, and prepositions, and (4) stylometric data based on univariate and multivariate statistics. Interclausal relations and structural irregularities seem to be the most noteworthy syntactic peculiarities.

Statistical analysis of these variables leads analysts to judge whether a particular work is truly Pauline or not. Obviously this is not an exact science, since people do change their writing style over time ("age"). Also, a letter dictated off the cuff to a secretary may be very different in style and syntax from on that is written and edited over a period of weeks ("orality vs. textuality"). Evangelical scholar Jermo van Nes identifies several other factors that may account for variation. These include the use of quotations and proper nouns, subjectivity, emotion, and topic. This chart expresses how such an analysis is mapped:

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The OP also asks: Are there examples of it being used to make a case for a "canon within a canon" by eliminating fraudulent letters (i.e. pseudepigrapha) existing in the commonly accepted canon? The answer is yes in terms of some critical scholars dismissing certain letters as illegitimate, but not in terms of any particular denomination that I know of. The NABRE (authorized for Catholics) concludes its introduction to the Pastoral Epistles with the following:

If Paul is considered the more immediate author, the Pastorals are to be dated between the end of his first Roman imprisonment (Acts 28:16) and his execution under Nero (A.D. 63–67); if they are regarded as only more remotely Pauline, their date may be as late as the early second century. In spite of these problems of authorship and dating, the Pastorals are illustrative of early Christian life and remain an important element of canonical scripture.

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