Thanks for all you help.
Your suggestions reminded me a long time ago I encountered a strange problem and it was fixed by clearing system cache as suggested by Apple Support. I tried booting into Safe Mode a couple of times using instructions from Apple Start up your Mac in safe mode - Apple Support. But the problem remained.
When I double clicked on a PDF file, most of the time, it was opened in Acrobat. If I right clicked on the file and selected "Open With" and then the default application (first entry in the popup menu, which is PDF Expert), it opened with PDF Expert. If I selected "Other..." on the second popup menu and then "PDF Expert.app" in the application folder, it showed an error message.

When I clicked Open on the message, the file was opened in "PDF Expert". If I tried other files, they still opened in Acrobat.
I tried to override application security on "PDF Expert.app" by holding down <Ctrl> while clicking on the application according to this article https://www.lifewire.com/fix-developer-cannot-be-verified-error-5183898. It did not change the behavior. Note that I used PDF Expert for many years and I know it is safe. The last update of the app happened in July 2022, and I opened the app dozens of time every day. The problem was caused by the latest Ventura 13.1 update.
After all the experiments failed, I went back to P. Philips' suggestion. On the Info page, I changed "Open With" to Acrobat. Then I changed it back to "PDF Expert". It worked. Now all PDF files are opened with the default app.
Since there were quite a few things I tried, I cannot tell which step(s) fixed the problem. I am recording the steps here hoping it will help someone else in case they encounter similar problem.