cant create work profile when device owner exist

Yes, only private device with work profile (BYOD) or COPE or fully managed is possible. You can't combine.

Hi, thanks for your reply. but in Android 10 or Android 11, I can have a device owner and managed profile together.

for example, I install the Google test-dpc app on my device and set it as device owner with adb or scan qrcode. after setting up this I can create a managed work profile. but in Android 13 I cant 

I have to say: I never tried but it doesn't make sense.

Why?:

BYOD (Bring Your Own Device) = A private device where nearly nothing is manageable regarding device settings but able to provide work apps etc. to a device owned by the employee. Finally: Work profile is already present and on such a device no one from the company has to manage/get access to the private part of the device (DO is the employee).

COPE (Company owned Personally enabled) = A nearly fully managed device but with a work profile on it, so private device with work part but with more access for the admin to setup device settings than on a BYOD device as this device is owned by the company. Finally: Work profile is already present on this type of device and on such a device no one from the company has to get access to the private part of the device (DO is the company but provides a private section for the employee).

COBO (Company Owned Business Only = fully managed): You have entire access to the device and it's settings and files. As you don't want as a private person someone get's access to the private part and this device is already entirely setup as a "work" device (with no private seperate section) there's no need for a work profile. (DO is the company and there's no private section)

So, in general it more looks like you are using wrong enrollment type as every possiblity is given here. I think you want to have a COPE device enrollment (factory reset before enrollment needed if your device was enrolled different before).