I don’t think we’ll see WW3 erupt from this. A military aircraft on a military mission gets shot down - it happens. Civil transports flying on airways have been taken out without starting an immediate conflict between nations.
At what level was the decision to fire taken? Behind the scenes the Turkish government is likely furious but equally don’t want to lose face with a frantic apology. How would “poking the Russian bear”, as another poster put it, advance Turkey’s interests? It doesn’t make sense from a premeditated standpoint.
Also, although they are a longstanding member of NATO, little things like human rights, the invasion of Cyprus and the unfortunate fact that not many in the EU want them any closer may play against the Turks. The Ukraine gave up nuclear arms in exchange for western support and look what good it did them...