3b οὐκ ἐπ’ ἄρτῳ μόνῳ ζήσεται ὁ ἄνθρωπος
This was quoted verbatim by Jesus in Westcott and Hort (NA27 variants), Matthew 4:
4b Οὐκ ἐπ' ἄρτῳ μόνῳ ζήσεται ὁ ἄνθρωπος
Did Jesus establish in Matthew 4:4b that LXX add words to Deuteronomy 8:3b?
No, this can be explained by NT manuscript variants. Some has the article; Some don't.
Now onto the the second more serious part of the question,
3c ἀλλ᾽ ἐπὶ παντὶ ῥήματι τῷ ἐκπορευομένῳ διὰ στόματος θεοῦ
None of the Greek manuscripts in
https://biblehub.com/multi/matthew/4-4.htm has the article τῷ in it.
Does this missing article change the meaning?
I don't think so.
Noun - Dative Neuter Singular
Strong's 4487: From rheo; an utterance, ; by implication, a matter or topic; with a negative naught whatever.
Verb - Present Participle Middle or Passive - Dative Neuter Singular
Strong's 1607: From ek and poreuomai; to depart, be discharged, proceed, project.
The mising τῷ is the Dative Neuter Singular of the Greek article. Pramatically, it is clearly implied by the two surrounding Dative Neuter Singular words.
Did Jesus establish in Matthew 4:4c that LXX add words to the Hebrew Deuteronomy 8:3c?
No. The words here are articles. We are not talking about adding a verb, or a noun, or an adjective.
Deuteronomy 8:3c was orignially written in Hebrew. LXX translated it into Greek. There is no 1-to-1 correspondce between the usage of Hebrew and Greek articles.
Did Jesus establish in Matthew 4:4 that the later LXX editions add words to Deuteronomy 8:3?
Wether he did or not, the meanings have not changed. Often, NT writers did not quote OT texts verbatim anyway. It was okay as long as the inspired meanning was brought out.