How large should PCB traces be to control a solenoid?
7W at 12V comes up to around 0.6A. Round up to 1A for safety, then calculate the required trace width using one of the various calculators.

The first calculator I found on Google gives me 30 mil for inner, and 11 mil for outer layers with 1 oz/ft² copper, so these should be fine.

On a board as simple as this I'd probably go Copper Thieving and create huge zones instead of traces.