For disability, you stop working at your current employer or…

Thanks for the clarification.

EDD are sticklers about what constitutes work. From a legal perspective, an applicant risks being ineligible for benefits if he/she does any work-like activity. CA EDD has a detailed list as follows:

Eligibility for Disability Insurance
Disability Insurance benefits can be paid only after your employees meet all of the following requirements:

The individual must be unable to do their regular or customary work for at least eight consecutive days.
The individual must be employed or actively looking for work at the time they become disabled.
The individual must have lost wages because of their disability or, if unemployed, have been actively looking for work.
The individual must have earned at least $300 from which State Disability Insurance (SDI) deductions were withheld during a previous period.
The individual must be under the care and treatment of a licensed physician/practitioner or accredited religious practitioner during the first eight days of their disability. (The beginning date of a claim can be adjusted to meet this requirement.) The individual must remain under care and treatment to continue receiving benefits.
The individual’s physician/practitioner must complete the medical certification of their disability. A nurse practitioner may certify to a disability within his/her scope of practice however, he/she must perform a physical examination and collaborate with a physician or surgeon. A licensed midwife, nurse-midwife, or nurse practitioner may complete the medical certification for disabilities related to normal pregnancy or childbirth.
If the individual is under the care of an accredited religious practitioner, they may download and print the Claim for Disability Insurance Benefits-Religious Practitioner’s Certificate (DE 2502) (PDF).