Reverting to the previous operating system will require you to wipe your startup drive, install macOS Ventura, and then perform a migration from a current Time Machine backup. That will be expensive with your nervous system and time investment. I advise against this endeavor.
If you are using any Anti-virus application, or so-called Mac cleaner application, you should first follow the vendors instructions for fully removing them, reboot, and try Pages again before you proceed with LibreOffice.
The LibreOffice 7.6.3 installer simply asks that you drag and drop the LibreOffice application onto the Application folder alias to the right of it. There is nothing about that installation process that could possibly cause your iPhone to dial.

Next, you Eject the LibreOffice installer icon from your Desktop. Then, in the Applications folder, you right-click once to open (not open with) on the the LibreOffice icon; it tells you it is an application downloaded from the Internet, to which you click OK, and the Office suite then launches. You can then quit it, or use the Open dialog to try opening your Pages document.