Nagorno-Karabakh is an 'Armenian enclave' inside Azerbaijan, which seceded from Azerbaijan in the 1990s, and has some kind of unclear status of autonomy since a ceasefire agreement in 1994.

See https://en.wikipedia.org/wiki/Nagorno-Karabakh

and https://en.wikipedia.org/wiki/Nagorno-Karabakh_Autonomous_Oblast

Azerbaijan and Armenia have different time zone rules, represented in TZ by Asia/Baku and Asia/Yerevan.

Has anyone researched the time zone and DST rules in Nagorno-Karabakh?

If the time zone rules followed locally differ from Azerbaijan, the situation there justifies the creation of a separate TZ zone. The zone exists now since 25 years with rather high political stability.