I tried to search via Ctrl + F → Log message and it returned me a list of microflows where the activity was used and some other stuff (as I added the search to include everything). This worked perfectly fine with Mx 7.
However, when I try to do the same thing in Mx 9.6 it does not return anything. Seems like a bug maybe.
If you can also confirm this behavior, I’d suggest raising a support ticket. Though, I don’t have other ideas on how to resolve your issue in the same version!
While this isn’t a answer to the question of finding all the Log Message actions in a project, it may help with what you are trying to achieve.
If you are familiar with Java, there is a method in the Core API called registerLogSubscriber. This allows you to hook into every call to the standard Log Message action. If you are looking to extend logging functionality this would be the ideal place to do it.