it is an error message of some kind. I haven't had an Event like that but I have had it for training at the Gym. I have started a thread in Problems & Bugs about it, so staff will be able to find out about it when they have a moment free.
So far, it doesn't seem to be preventing me from actually training my pets in Chrome, it just makes for a lot of scrolling to get down below all the error messages. I'm getting two per pet so that's a lot for me. What Event it is replacing for you I do not know, sorry.
just posted in Site Updates that they are converting the site to use an app called docker. We may be seeing warnings like this until they update PHP and it propagates throughout the site.
It is my belief that Subeta does a really good job of updating your account and keeping it saved. I think caring about your pets is a good idea though. . There might be a place in Prefs for you to save your account data to your own computer or force a save if you are concerned.
You mentioned you can download your account data; I thought that was disabled a few years ago?