You could apply for the residence permit via the WeChat mini-program "Suishenban".

Search "Suishenban", select the Exit-Entry column and then the Visa/stay permit/residence permit.

You could also apply for the Issuance of foreigner's residence permit via the following online platform.

Government Online-Offline Shanghai

Please register first for an account number.

Open the website of Government Online-Offline Shanghai and click "Register now";  

Finish the registration step-by-step;

After registration, you can login to the homepage of the Government Online-Offline Shanghai.

Click the Guide for Newcomers to Shanghai from Outside the Chinese Mainland.  

Click the button "Foreigners" and enter the page;

Click the button "Foreigners" again;

Click on the "Issuance of foreigner's residence permit" and then apply. There are eight different scenarios for work-related residence permits, including the one-year residence permit for work, two-year residence permit for work, three-year residence permit for work, four-year residence permit for work, five-year residence permit for work, residence permit for work (marked"high qualified person" ), residence permit for work (marked "internship"),and residence permit for short-term work.Through this route, you can also handle the Change of residence permit information.