Unfortunately, as a general rule, when an employee quits they will be disqualified from receiving unemployment benefits. This is because one of the requirements for receiving benefits is that the claimant be unemployed "through no fault of their own." When an individual quits, they are generally regarded as unemployed "through fault," since they made the voluntary decision to become unemployed.
The only exception to this rule is if you could demonstrate that you quit for reasons amounting to "good cause." However, this is a very high standard that requires you to demonstrate that no reasonable persona would have remained employed under the circumstances. Candidly, the facts you have described are unlikely to meet that standard, even though the circumstances are understandably quit frustrating and you are completely right to no longer want to work there.
If you are on an unpaid suspension, you can apply for unemployment benefits now--it doesn't matter whether you have formally been "terminated." There is a one week "waiting period" for UI benefits so if the suspension does not exceed one week you won't get anything, but it can't hurt to apply.
Otherwise, it would be prudent to start looking for new work now and quit only once you've secured an offer of employment somewhere else. It will also be easier for you to find another job while you are still employed, as studies have consistently shown that employers prefer to hire applicants whom they perceive to be "in demand," already working somewhere else
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