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The schematic shows a 11-0-11VAC secondary, and an extra winding for the dial lamps 300mA which is usually 6V. The guy just jumpered them to 11VAC and if they are way too bright, add a resistor or put the lamps in series.
I would estimate 15-20VA, it's not much current, mostly for the motor. If mains voltage is high then 13-0-13 might be too much voltage and IC11 etc will run hot.
The big problem is the tape head will pick up AC hum from the transformer, so it is customarily located far away and oriented at an angle for the least hum.
Best to get a transformer that fits on the PC board? The new one looks a bit big and the laminations seem to have a lot of air gap between them. I wonder if it's handmade.