It’s an interesting question. OED covers some aspects of this under have, v. II
As an auxiliary verb. As in the other Germanic (and Romanic) languages, the various moods and tenses of have are used with the pa. pple. of another verb, to form a series of compound or ‘perfect’ tenses of the latter, expressing action already finished at the time indicated, and answering to the Latin perfect tenses dedi, dederam, dedero, dedisse, etc.This use arose directly from sense 2b, the object possessed having in agreement with it a passive participle of a transitive verb as attribute or complement; thus, I have my work done = ‘I possess or have my work in a done or finished condition’, whence, by inference of antecedent action from result, the actual sense ‘I have done my work’: cf. the series ‘have you the article ready?’, ‘have you the article completed?’, ‘have you completed the article?’ In some dialects the distinction between the original and developed forms, e.g. ‘He has the house built’, ‘he has built the house’, is still in regular use; with some past participles, as begun, completed, done, finished, etc., it is recognized generally. With transitive verbs the developed use was already frequent in Old English; the pa. pple., which originally agreed in number and case with the object, was sometimes left uninflected. In early Middle English the usage is found with verbs of action without an object, whence it was extended to intransitive verbs, especially, at an early date, to the verb to be (as in French and other Romanic languages, and in opposition to continental Teutonic use), as he has been, had been, will have been, etc. (cf. French il a été, German er ist gewesen). Verbs of motion and position long retained the earlier use of the auxiliary be; and he is gone is still used to express resulting state, while he has gone expresses action.
Here’s sense 2b, referred to above, with early cites.
b. with adverbial or other complement, particularizing the relation of the object or expressing some qualification, condition or limitation thereof.
c1000 West Saxon Gospels: Matt. (Corpus Cambr.) iii. 9 We habbað abraham us to fæder.
c1000 West Saxon Gospels: John (Corpus Cambr.) viii. 41 We habbaþ anne god to fæder.
c1290 Beket 2042 in S. Eng. Leg. I. 165 Ȝe to þe kingus wille is bodi ȝe habben al-ȝare.
1388 Bible (Wycliffite, L.V.) 1 Tim. iv. 2 That..haue her conscience corrupt.
a1400 (▸a1325) Cursor Mundi (Vesp.) l. 15317 He þat has his bodi clene.
1474 Caxton tr. Game & Playe of Chesse (1883) ii. iv. 45 A knyght whiche had to name malechete.
1526 Bible (Tyndale) Matt. iii. 4 This Jhon had his garment off camels heer.
1526 Bible (Tyndale) Matt. xxii. 11 A man which had not on a weddinge garment.
1583 C. Hollyband Campo di Fior 183 As long as we have this monkey to our cooke.
1597 Shakespeare Richard III ii. i. 113 When Oxford had me downe, he rescued me.
1634 T. Herbert Relation Trav. 3 They vsed to haue their Wiues in common.
What I find confusing is that many of the cites for the auxiliary verb usage predate those for sense 2b, which seems to conflict with the statement, “This use arose directly from sense 2b”, etc. I’m sure I’m missing something.