Plywood is fine for a transom. There are several areas where plywood is superior to the foam cores (compressive strength, ability to hold a screw, and ability to absorb resin and bond to laminate/skin). Penske/coosa is great for transoms, but plywood is proven to last for 30+ years with poly resin (even with poor installations).
Here's some home cheapo Arauco plywood acx I used in my bracket. Did my 23 transom with the same wood . . . come see me in 30 years

$30 sheet.