I believe (if you have the option) you can setup a Retool API token and then create an OpenAPI resource using Retool's schema and the newly created token.
One of the many endpoints that you can access with the proper scope is the /usage set which can be used to access pretty much exactly what you are asking for:
Thanks for these great solutions to tracking app usage per user.
Just to add some pricing/plan info here -
As @MiguelOrtiz mentions, if you're self hosting, you can query your own database that powers your Retool instance. This is true for all self hosting plans from Free up to Enterprise.
Again as @MiguelOrtiz mentions, if you're on Retool Cloud, you could work around the limitations by creating your own logs. This is the best workaround if you're on Retool Cloud's Free, Team, or Business plans.
If you're on Enterprise (Cloud or self hosted), you can take advantage of the full Retool API, as @pyrrho demonstrates
Note that these solutions only work for apps that require authenticating into Retool. We don't have any way to track user information on public apps.