I solved the problem by granting Full Disk Access to /usr/bin/ruby, as suggested here. /usr/bin/ruby launches Emacs.app so the launched app will derive its permission from those for ruby.

I solved the problem by granting Full Disk Access to /usr/bin/ruby as suggested here. Quoting from the reply,

Emacs.app actually launches using a ruby script. As a result, MacOS Catalina uses the permissions set for ruby, not the permissions for Emacs.app.

Grant access as follows.

• Go to "System Preferences -> Security & Privacy -> Privacy"
• Select Full Disk Access from the left menu. It is about half way down in the menu. A list of apps will appear in the main region of the window.
• Click the lock on the lower left and authenticate in order to allow making changes.
• Click the + button under the list of software and select /usr/bin/ruby.
  • /usr is usually a hidden folder and may not appear by default. If so, press shift+cmd+. (the last one is a dot) at the root directory to make it appear.

Emacs.app should now be able to access the file system without any hindrance!