From what I understand the employee should receive a Form 1099G from the EDD if they must claim it on their taxes and it would not be something that you need to include on the W-2. The information below is what I found in the edd.ca.gov FAQ and seems more geared toward the employee as opposed to the employer.
The Form 1099G reports the total taxable unemployment compensation issued to you from the State of California Employment Development Department (EDD) for a calendar year. Total taxable unemployment insurance includes:
Unemployment Insurance (UI) benefits – shown as UI.
Disability Insurance (DI) benefits received as a substitute for UI benefits – shown as DI.
Disaster Unemployment Assistance benefits – shown as DUA.
Paid Family Leave benefits – shown as PFL.
Your benefits are taxable and reportable on your federal return only, but you do not need to attach a copy of the Form 1099G to your federal income tax return.
Benefits are reported based on the issue date of the payment, not the week ending date(s) that was paid.
This information is reported to the IRS. If you are required to file a federal tax return you should report the amount in Box 1 of Table A and/or Table B of the Form 1099G as income and the amount listed in Box 4 of Table A as federal income taxes withheld.
Disability Insurance (DI) benefits are not reportable for tax purposes except when considered to be a substitute for unemployment compensation when paid to an individual who is ineligible for unemployment insurance (UI) benefits solely because of the disability. Only in this instance, where DI benefits are received in lieu of UI benefits, will the EDD provide the claimant with a 1099G form showing amounts paid which are reportable (no more than the original UI maximum) and forward a copy of the 1099G to the Internal Revenue Service (IRS).
Paid Family Leave (PFL) benefits are reportable for federal purposes but not state tax purposes. The EDD will provide all claimants with a 1099G form and forward a copy of the 1099G to the federal IRS. The PFL benefits are not taxable or reportable to the California State Franchise Tax Board.
I hope this helps.