Without getting into any details this: "Once in a group chat, team members referred to a new Asian American recruit as slanty eye joe" seems very strange to me. The Uber tech org is like 80%+ foreign born, this makes pretty much zero sense. Disclaimer: I work for Uber.
You work for Uber but are you in the SV offices? The culture probably varies quite a bit depending on where you are.
I have worked for a number of old generation US companies and some were a part of the military-industrial complex. The employee population in them was significantly biased to the right (white, male, middle aged), up to the point that it would be "Trump crowd" today. Yet, I have never heard anything like this. Uber as any other tech company is full of younger and more liberal people. So this particular allegation (open expressions of racism towards Asian Americans) just seems extremely unlikely.
Unless... Well, there are indeed some countries that are culturally very casually racist. Ex-USSR comes to mind. Yet, even ex-USSR crowd is not that stupid and by now there enough self awareness to not say things like this out loud.
This is fishy.