I basically play Franchise only.
When I start a zoo, i do get some notifications concerning staff not able to reach staff room but they disappear pretty fast.
I have no issues with staff not replenishing their energy but all staff buildings are connected with the staff path.
I always replace the normal path with the staff path, when it comes to staff/energy facilities.
Personally I think if you connect a staff building with a staff path, it should automatically pick the same path for the connection. (or did i miss an option ?

)
Maybe for some users replacing that small piece "normal path" right outside the facility could fix the issue?
In earlier comments that fixed it for 1 user.
And in a lot of screenshots it shows that people mix normal paths with staff paths. At least it's worth at try (for some)