After a quick search for the manual it looks like this to me:
You have connected the Shelly to the output of the transformer. (24VAC). In order for it to work with the Shelly 1, you have to connect it to 24VDC. See photo:
Sorry, after reading a little further, I see that this connection is for a relay. Unfortunately the plan does not give the information, where to find the 24VDC. I think, it is available in the right terminal with the numbers 20,21,5,23, but to be sure you have to measure it. I think, it is between terminals 20 and 5, no idea, which one is plus or minus.
Maybe the current is not enough for the shelly, then you have to take a Shelly Plus 1, which you can connect to 230VAC.
This is not allowed with the Shelly 1 you have, see #2 from Devil.
In your case you could also take a Shelly Uni, which you can supply with 24VAC.
Or you put a full bridge rectifier and a capacitor between transformer and shelly...
Next edit: I thought, I have already seen this door gate, so, after a search in the forum I found it.
Terminal 20 is 0V, Terminal 5 is 24VDC.
But the voltage drops, when the gate is driven. So the best solution is a Shelly Plus 1, but please ask for some help, when you connect it, your wiring looks not very good to me...