In California, Covid relief was extended until the 12.31.22, can I deduct that gross income from my federal taxes

What gross income?  W2, 1099, etc?

No - this is a state of CA program and not a federal program.  There is nothing to deduct on the federal return related to this program. 

https://www.dir.ca.gov/dlse/covid19resources/2022-covid-19-SPSL-Poster.pdf