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Be Transparent With The User
Since we are talking about logging, another thing you must do is to be transparent with the user in your user interface.
And by "be transparent", I meant that your website/mobile app needs to point out to the user that the webserver is down instead of saying to the user to check their internet connection; your application is getting something from the webserver, so you can say "Oops, something wrong on our side".
Another example: If you need to check a bunch of data before saying "It's done", add a counter to show the user that the application is doing something. Joplin, when syncing data with a webdav server, needs to check a bunch of files; one version would simply sit still with a spinner on "Syncing" and nothing more; when they added a counter, I could easily see that there was something going on.
Those small details, for as bad as they may make you look, will win points with the user in the long run.