Unable to open Apache Open Office on MacBook Air with macOS Sequoia 15.0.1

FWIW, OpenOffice has been dormant since 2015. I would uninstall it and install the free LibreOffice which does work with Sequoia.

You should update to the current Sequoia 15.3.1.

Here is an additional comment for you. It is helpful to understand that when any app is installed, it can only be opened if the app's version is one that is compatible with the installed operating system. If it is not, then the app must then be updated to a version that is compatible.