Why would I be eligible for unemployment benefits through NYS Department of Labor?

You likely qualify! For NYS Department of Labor unemployment benefits, you need to meet a few basic requirements: 1) You must have lost your job through no fault of your own (layoffs count), 2) You need sufficient work history and earnings in your 'base period' (usually the first 4 of the last 5 completed quarters), and 3) You must be able and available to work. Since you worked 8 months and were laid off, you should definitely apply. The worst they can say is no, but based on what you described, you have a good chance of approval.

Don't listen to your friend about not being there long enough - that's not how it works. NYS Department of Labor looks at your total earnings across ALL jobs in your base period, not just your most recent job. If you had other jobs before this one, those earnings count too. Even part-time work counts toward your eligibility. You should absolutely apply as soon as possible since there's a waiting week.

I was in a similar situation last year - got laid off after 10 months at my job but had worked other places before that. NYS Department of Labor approved my claim pretty quickly. The key thing is being laid off versus being fired for cause. Since you were laid off due to budget cuts, that's definitely 'no fault of your own' so you should be good there. Just make sure you file your weekly claims on time once you're approved.

If you're having trouble getting through to NYS Department of Labor to ask questions about your eligibility, I had success using Claimyr (claimyr.com) to actually reach a real agent. They have a video demo at https://youtu.be/qyftW-mnTNI that shows how it works. I was getting nowhere with the regular phone system but this got me connected to someone who could explain my specific situation. Might be worth trying if you want to talk to someone directly about your eligibility before filing.

just apply already!! worst case they say no but if u were laid off u probably qualify. i got approved after working only 6 months at my last job but had other jobs before that so it all counted

The unemployment system is set up to help people exactly like you - workers who lose their jobs through no fault of their own. Don't let anyone discourage you from applying. NYS Department of Labor will review your work history and earnings to determine your eligibility and benefit amount. Even if your weekly benefit is small, it's still money coming in while you job search. File your claim online through my.ny.gov and see what happens.