Without knowing more about your architecture, this would come down to whether or not you want to expose logging database to your frontend. Your options are:
- As you said, make a subsequent request to the server, which may or may not succeed, but probably has a higher likelihood of succeeding. I would chose this if I didn't want to expose my log storage to the frontend
- Setup a clientside log storage. AWS Rum is what I've used in the past. In fact, I'm using AWS Rum with a Vue application for a client right now
By using Rum, you can choose to store only Frontend errors in the frontend log storage, and reserve the backend log storage for server side issues.