Processes in Microsoft 365 for setting up Office apps, redeeming product keys, and activating licenses.
Unfortunately your looking for a 100% guaranteed definitive solution to eliminate a problem which regrettably doesn't exist. My original post contained the following
"Error 30045-25 is typically indicative of a previous failed uninstall of Office? Is a previous Office uninstall applicable in this case? "
Your response was that indeed 2010 did exist on your system. My follow-up response provided options for two scenarios - a side-by-side install config which is is not recommended (but allowed) at the best of times but would require a repair of 2010 without uninstalling it or a stand-alone install of '2016 requiring the uninstall of '2010 in which case you would need to uninstall '2016 and then re-install '2010. Repairing '2010 would have no impact on the operation of '2010.
You are absolutely correct that this is a "trial & error" suggestion since there is absolutely no way for anyone to know with 100% absolute certainty of what the cause is but regardless of cause, it would still require some action on your existing 2010 install (given the error message) no matter which of the two scenarios you opted to follow.
On that note, will have to leave this to someone else in hopes that they have an answer you're looking for that differs from my suggestions and that will be guaranteed to be correct with 100% certainty. My only final suggestion that would provide the security you're looking for is to install '2016 on a different computer for testing purposes.