What's the max current of a power adapter that's rated at 24V Max 7W if I regulate it down to 3.3v?
Does it matter if I regulate it down to 3.3v (probably linear) ...


Linear will have the same current limit as the supply.


  ... or will the max current still be 290mAh?


'mAh' is a measure of current by time and usually used for battery energy specifications or use.

\$ I = \frac {P}{V} = \frac {7}{24} = 0.29 \ \text A\$. 290 mA is the correct answer.