OED:

Periphrastic Adj.

Compound - periphrastic conjugation n.

Grammar a conjugation formed by the combination of a simple verb and an auxiliary, rather than by an inflection of the simple verb.

1874 Presbyterian Q. & Princeton Rev. July 449 We find a so-called periphrastic conjugation, ic maeg, can, mot, scyle, ‘I may, can, must, shall, &c.’

1984 Amer. Jrnl. Philol. 105 413 Periphrastic conjugations emerged as substitutes for the now much weakened monolectic perfect.

See also https://www.thoughtco.com/periphrastic-grammar-1691610 = Periphrastic Constructions in English Grammar.

(I often think that Pullum & Huddleston delight is being contrarians on the basis that you can only be called a grammarian if you have your own theory - if you agree with someone else, you are merely an acolyte...)

Additional

https://www.collinsdictionary.com/dictionary/english/periphrastic

periphrastic in British English

Adjective

2. expressed in two or more words rather than by an inflected form of one: used esp of a tense of a verb where the alternative element is an auxiliary verb. For example, He does go and He will go involve periphrastic tenses

and

https://www.oxfordlearnersdictionaries.com/definition/english/periphrastic

periphrastic adjective

2 (grammar) using separate words to express a grammatical relationship, instead of verb endings, etc.

Auxiliary verbs also called as helping verbs/helper verbs.

For Example # I have completed my today's Todo-List.

Here, main verb = complete and
helping/auxiliary = have, which used to express complete meaning of sentence.

source:https://en.wikipedia.org/wiki/Auxiliary_verb