Nice looking mulch, how long ago was it that animals were last there (if you happen to know?) On one hand I'd be tempted to clear it out "just in case" and then replace it with similar, but on the other if there is any bacteria, parasites, etc. it's probably in the soil too so removing the mulch is only going to go so far.
I feel like adding a fresh layer of tanbark or whatever "bedding" (can't think of the right word for when it is for the run) you choose might be a good middle ground. That is what I would do however I've not had to consider this as my coop is a new build with no previous animals on the property.