To take this example, the Azerbaijani president didn't talk the American one into a major shit show of a war; one that is materially harming American lives. The Azerbaijani government doesn't run a major political influence operation in the US, spending 10s of millions of dollars against candidates for the sin of mildly criticizing them. The Azerbaijani government doesn't receive anything close to the level of military, diplomatic, and financial support from the US that Israel gets. The Azerbaijani prime minister didn't give an address to the US Congress to undermine a major foreign policy agreement, one which has only looked better in hindsight.
So no, it's not at all weird that the citizens of the US care more about Israeli committed atrocities than Azerbaijani ones. The US is far more involved with Israel's actions and has far more influence over them, influence that has so far not been used to try and alleviate the suffering in Gaza.
The Biden administration paused diplomatic relations, put out public states condemning it, and more.
In fact, Azerbaijan came out and complained about the US's "biased" stance against it.
https://asbarez.com/aliyev-criticizes-biden-for-biased-towar...
What an argument.
Save it.