Working Multiple Jobs Being a Permanent Resident

[FNC]

Hello,

I have one job currently from big tech (FAANGM) company in Seattle WA and I have another fully remote job from manufacturing sector (different industry compared to my current employer). I have a green card (permanent resident).

1. Is it allowed if I will be applying for paternity leave (receiving state benefits from Washington State from one company where I am currently working ) and simultaneously working for another company remotely (fully remote job)? Wanted to understand if it is allowed legally?

2. Wanted to understand if is it legal to paternity leave benefits from Washington State while working for another fully remote job being a a permanent resident (i.e., I have a green card) or is it not allowed and considered illegal?

3. Let me know if I need to be aware of anything for this or any complications or something can happen due to this that I should be aware of? Or any issues for naturalization (citizenship)?

Please guide and give advise. Thanks a lot.