I wonder if Mr.Cagaptay can show me a single sentence used by Stalin containing the word "Азери" (Azeri) in refer to Azerbaijanis? https://twitter.com/SonerCagaptay/status/1337412331194683392

While "Azeri" was not used in Russian Empire or Soviets, "Azerbaijani" had an older history. It was used in Jalal Unsizadeh's Kəşkül in 1883 as part of more complex "Azerbaijani Turk".

Later in 1891, Shahtakhtinski argued that "in everyday life, it is inconvenient to call a people or a language in two words - an “Azerbaijani Turk” or an “Azerbaijani Turkish”. Therefore, it would be more appropriate to call it Azerbaijani" https://medium.com/@cavidaga/how-to-call-transcaucasian-muslims-c6c753c782d5

A book from 1889: Azerbaijani title reads "Qüdrəti-xuda - Mübtədi məktəb şagirdlərinə məxsus və hüsni-əxlaqə dair Azərbaycan dilində risaleyi-qiraətdir" (Might of God - A reading material about morality in Azerbaijani language for primary school pupils)

Same book had Russian cover as well. It was named "God's omnipotence - A self-reading material in Tatar-Azerbaijani dialect".

Notice the lythography name - Kashkül. They were really dedicated to popularize the name "Azerbaijani" even among children.

First textbook for children was published in 1882 - "Vətən dili - Türki-Azərbaycan dilində təriqi-sövti üzrə təlim olunan əlifbaya müştəmil..." - mentioning Azerbaijani and Turkic together while Russian title said "Tatar alphabet of Azerbaijani dialect". Here is 1901 reprint.

Finnish academician Ivar Lassy, who researched Azerbaijani shiism and published a dissertation in 1916 also stressed that the no intelligent native would use misleading designation as "Persian", still in order to avoid confusion, uses more known term "Tartar".

It is a myth that Stalin invented the term Azeri or Azerbaijani, it is repeated by the well known fallacy "Stalin was a bad person, therefore everything he does should be bad!"
Azerbaijani as ethnonym was coined by Azerbaijanis themselves.
We never called ourselves Azeri

Current use of "Azeri" by Azerbaijanis in is only for in English to shorten 11 character long "Azerbaijani"
Stubborn use of Turk instead of Azeri in is a reaction to constant nationalist tale of them being Turkified and therefore 'a need' to de-Turkify them.

Hope that would be final explanation.