First, thank you for your prompt reply! I agree with your classification for absolute majority of examples you provided in your answer.=)

So, let me highlight the trees I feel disconsent about.

I'd argue that
- Parpetsi street (https://www.openstreetmap.org/way/380363605)
- Koghbatsi street (https://www.openstreetmap.org/way/82550803
- Teryan street (https://www.openstreetmap.org/way/133144300)
- Hin Yerevantsi (https://www.openstreetmap.org/way/371569595)
- Spendiaryan st. (https://www.openstreetmap.org/way/360172405)
- +maybe other streets I not have spotted, because I did not do an exhaustive check=)
- ~maybe~ even streets like Tamanyan (https://www.openstreetmap.org/way/26374568)

...are tertiary along their entire length. My "feel" that these roads satisfy definition in Ru-wiki of tertiary road: "главные улицы по отношению к прочим мелким улицам/переулкам, основные микрорайонные или межмикрорайонные транзитные улицы" as well as En-wiki definition of tertiary (and less so on residential)

Those listed streets are less prominent than, say, tertiary road of Tumanyana (https://www.openstreetmap.org/way/379702959), but they are still:
- serve much more for "through" traffic rather than access to neighbourhoods
- they do not have speed limits or calming measures other than their width
- very similar in role and appearance to tertiary road Pushkin street (https://www.openstreetmap.org/way/133082150)

PS: my perception, is that in your edit you prefer to keep classes so that hierarchy prevails: residential should flow into tertiary, tertiary into secondary, etc. So, (in my perception) you define the Tertiary class relative to its connections; while I think that at the level of Tertiary road class hierarchy principle gives way to the functional definition.
*I have not read anywhere, if one or another approach is preferred, so I don't know)