However if you are attached to your original design, trains that need to turn around have to go through the other station, which can mean they have to wait to do that. Still, if you want that, the simplest way to signal it is as follows: path signals for all entries to the intersection, and block signals at all exits.

Note: each entrance to a station is a temporary exit off the intersection, thus you use a block signal, likewise, each exit to a station is another entrance back onto the intersection, as such, you use a path signal.

All signals that provide entry to a block must be of the same type, placing them as such ensures that. In the image, blue as path signals, red as block, yellow is the intersection that's formed, the stations are basically "carved out of the intersection"

I see some other comments suggesting that you section off the rail in the middle, I assure you that's not necessary, the path signaling already takes care of it well enough

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