The fuse for the supply is 1 A, so that represents 120 W. You need a 120 W or larger trnansformer.
You could use this:-
https://www.newark.com/multicomp-pro/mcta160-18/toroidal-transformer/dp/38K4911
View attachment 147034
The 36 V input would be what would normally be the secondary and you need to wire the two windings in series. That would be done by connecting red to orange and connecting black and yellow to the 36 V ac supply.
The two 115 V windings, marked as primary but being used as the the secondary, would need to be in parallel. Wire blue to violet and to the live connection of the load. Wire grey to brown and to the neutral connection of the load.
The dots on the winding diagram are important, and you cannot swap one winding (eg blue to grey) if it is connected to another winding.