Greece-Turkey conflict will stay dormant as long as these two countries are part of the NATO.
There is a lot of old conflicts that are surfacing these days though. Some countries are even bringing up WWII issues, conflicts over territories, etc. They've also started the process of kicking out Turkey (US accused Turkey of war crimes in Syria after all this time of knowing it!!!).
But I agree that Greece-Turkey conflict will remain dormant. Right now Turkey has a purpose to server which is to connect to Baku by occupying parts of Armenia then they can add Baku to NATO immediately to gain a huge advantage (as I pointed out before, which also affects China). If they fail, Turkey's importance to NATO significantly decreases depending on how they failed. For example there is a good chance that the moment Turkey gets involved in this conflict inside Armenia they will see themselves in a whole lot of hell coming from Syria and Iraq (south borders) and Iran inside Armenia and possibly directly on eastern border. Turkey's economy and energy sector would simply vanish with no gas and oil and possibly even 200%+ inflation.
Some analysts are suggesting that this conflict would be prolonged for months where Turkey is sucked in and destroyed slowly. Keep in mind that they have a big military but it is the most dependent military considering that almost everything they have is imported. EU and US are already complaining about empty weapon cashes due to the tremendous amount of weapons they've been sending to Ukraine. So there won't be anything left to send to Turkey.
Which could be another incentive to kick Turkey out of NATO (winter is also coming!), they just call their invasion of Armenia another "war crime" and kick them out.
That also means NATO won't have to get involved when Turkey's mainland is hit in respond to their invasion
Then Greece (ie. NATO) goes after Turkey and may not even need an armed conflict, they just take parts they want without shooting a single bullet.
Full invasion of Armenia may not be needed. All they (Azeris) need is to conquer around 200-300 sq.km of territory between Naxçıvan and Zəngilan.
It looks easy on paper. We are talking about a mountainous territory that is extremely hard to cross and an uphill battle where Armenia has the upper hand and can rain missiles and bombs on their heads all day long.
In any case we have to wait to see what will happen. Right now there is all kinds of fake news coming out and it looks like every military in that little region is mobilized already...