US tax return after returning

I moved from US to India this September. Started my Indian job in October. As I understand I will be US resident alien for 2021 tax year.

My question is do I need to declare salary earned from my new Indian job as foreign income on US taxes? I am planning to fill FBAR as usual.
If so, how do I claim exemption as it is already been taxed in India.

From what I understand, your global income is taxable if you are a US tax resident. I think you should be able to get the exemption, might need to look it up. I’ve done it the other way round only when I was an Indian tax resident and got an exemption on my US income in India.

Definitely talk to a tax consultant. Since you left the US for good, I think you have the option to either declare yourself as a part year resident or a full year resident.