I suspect that expansionist Erdogan would very much like to take over (annex) Armenia directly, or install a puppet (satrap) Government there - if it could somehow overcome or evade their Russian support.
Another chip on the table, in their growing string of Military confrontations.
Even if there is no chance of taking Armenia directly, this might be a wedge issue to pry away Azerbaijan (and it’s oil and gas) from Russia.
“Even if there is no chance of taking Armenia directly, this might be a wedge issue to pry away Azerbaijan (and it’s oil and gas) from Russia.”
Putin could, if pushed, do the same thing to Azerbaijan. Both it and Armenia were once part of the Soviet Union, and before that both were part of the Russian Empire. Putin sees both as within the Russian sphere.
NATO should see that Turkey is in GREAT error, and put Turkey’s NATO membership on the table unless Erdogan stops his Azerbaijan adventure. NATO surely has no interest or business in promoting the conflict and if it led to confrontations between Turkey and Russia directly, NATO nations could be treaty obligated to aid Turkey - which in my view they should not do. The better course would be before things get to that point boot Turkey of NATO.