Originally an Open Office user, I transitioned to Libre Office several years ago. My current version is 7.0.1.2 (according to Help). The current Libre version is 24.5 (or greater?). Can I download this updated version over my older version without risking access, operations, etc.?
The intention is indeed that new versions should work fine.
But there should be no one claiming that any upgrade of any software would be ever free of any risk. Bugs happen. Incompatibilities happen.
On the other hand, we have a download archive (see the very bottom of the main download page), with every single version released over the project history (and even with pre-releases). So you may always try a newer version (maybe you would like to backup your profile first), and if needed, revert to the version that you know works.