I was able to renew Federal Non-Compliant online without any hassle a week ago.I haven't received it on mail yet, but it didn't give any errors through the process either. Neither did it ask for any TPS documentation.
Is your current DL a REAL ID or Fed Non-Compliant? To apply for a REAL ID card, you must visit DMV. If you already have a REAL ID, great! You can follow the same steps for renewal online.
If you're only looking to renew a non Fed Compliant DL, create an account and apply for renewal: https://www.dmv.ca.gov/wasapp/dlir/dlirApplication.do
Hope this helps.