If Azeris claim to be descendants of Caucasian Albanians and Turkic tribes (you know, the whole "two brothers, one nation" thing), how is it possible to push both narratives at the same time?
Why doesn't anyone of them speak Caucasian Albanian? Why don't they use their alphabet?

Why was the Caucasian Albanian alphabet discovered at the end of the 20th century? What happened to the Christian Caucasian Albanians? Did they just vanish in thin air? Why are Armenian churches with Armenian inscriptions being attributed to Caucasian Albanian?

Here is the language tree of Altaic langues. You can see the Turkic languages. You can see Azerbaijani in the left corner below

Here is a specific language tree of the North Caucasian languages. Still no mention of "Caucasian Albanian"

Caucasian Albanian is an extinct language. How can Azerbaijanis claim to be their descendants yet the last remnants of that language were found in the 12th century?

Another interesting factor, the Caucasian Albanian alphabet was invented by Mesrop Mashtots, who also invented the Armenian and Georgian alphabet. Mesrop Mashtots was born in 362 AD and died in 440. Turkic tribes didn't begin their invasions of the Caucasus until the 6th century.

It's literally impossible to claim both narratives at the same time. If anything, the Caucasian Albanians are way more likely to have naturally merged with Armenians because they shared a common religion and culture. Everything we know about CA is documented by Armenian scholars.