The lakṣaṇa of ‘gauḥ’ in Hindu tradition is to be determined by seeing what our pūrvācāryas have commented on this,and not on pseudoscientific nonsense like ‘desi cows are associated with gold nanoparticles’, ‘A2/A1 milk’,etc.
“gōḥ sāsnādimattvaṁ lakṣaṇam” has basically been the definition since the time of Pātañjali (of mahābhāṣya fame).
Vidyāraṇya similarly quotes Pātañjali thus
tathā cōktaṁ bhagavatā patañjalinā mahābhāṣyē – atha gaurityatra kaḥ śabdō yēnōcyaritēna sāsnāmāṅgūmakakudakhuraviṣāṇānāṁ saṁpratyayō bhavati saḥ śabdaḥ
So ,our ‘gauḥ’ is any breed of cow that is humped with horns,and with a dewlap and tail. And not about A1,A2(I don’t think the rājan bhadravarman of champa near Vietnam,who was a śrotiya and boasted of performing vaidika rituals could have checked for A1/A2 or gold nanoparticles).
I discussed with others (like Hariprasad),who noted that there is no strong reason to deny respect to cows of foreign breed since they are all of the same jāti,one can at best to say that there is tārātmy within breeds of cows and that foreign breeds of cows have less abhimāni devatā sannidhyam. Also,we have consumed their milk for whatever reasons,so not slaughtering them and taking care of them till their death should be our way of showing upakāra smaraṇam.