Which languages were spoken in Anatolia and modern Turkey when Turkic arrived?

I’m touched by Anon’s A2A’ing assumption of my omniscience, but I’m going to Wikipedia here, to confirm my vague hunch that the Anatolian languages of yore were long, long gone by the time the Seljuks came to town.

Anatolian languages

and it is generally thought that by the 1st century BCE, the native languages of the area were extinct.

With one exception:

Pisidian language

Known from some thirty short inscriptions from the first to second centuries CE, it appears to be closely related to Lycian and Sidetic.

Sidetic language

The Greek historian Arrian in his Anabasis Alexandri (mid-2nd century CE) mentions the existence of a peculiar indigenous language in the city of Side.

(The inscriptions we have are from 3rd–2nd century BCE)

In particular, if there was any evidence of Cappadocian surviving, we would likely have heard something about it from the Cappadocian Church fathers. Early research into Cappadocian Greek went hunting for evidence of Cappadocian in the language; lots of amateur speculation ensued, but no professional thought it worth pursuing.

So our default assumptions remain: the Seljuks found Armenian and Greek. And whatever babel of Caucasian languages there is in Lazistan.