I tried your suggestion and here are the results:
- It worked on the new profile but did not work on my main profile.
- I tried changing from “Continue where you left off” option to “Open the New Tab page” on my main profile and relaunched Brave. The pinned tabs and a new tab were restored.
- I changed it again from “Open the New Tab page” option to “Continue where you left off” option and it worked!
- I already deleted the new profile since I do not need it anyway.
Thank you for the suggestion. The issue is now fixed. For future readers, just follow these steps.