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Unfortunately, you generally cannot collect benefits when you leave your job voluntarily. You need to be terminated for reasons other than "misconduct" so that the EDD finds you are unemployed "through no fault of your own." Even if you were let go, there is an additional issue posed by the fact that you would be out of the country. In order to collect benefits, you ned to prove that you are actively seeking new work, and when you are out of the country that is generally not possible. If you claim benefits through the EDD's online portal (every week you have to recertify your claim) and do so from overseas, the EDD will automatically flag your account based on the international IP address you used to log on, and you will be audited and asked to prove that you are actually seeking work. Unless you can prove that you are overseas for a specific interview, you will likely have your benefits revoked.
So, regrettably, it does not sound like an individual in your circumstance would be eligible for benefits. If you can prove that your depression and anxiety rise to the level of a disability, meaning you are physically incapable of performing work, you may be eligible for State Disability Insurance, which does not require you to be unemployed through no fault of your own or actively seeking work. But you would need a doctor to declare you disabled. See here to initiate the SDI process.
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