So my front derailleur gets rubbed on by the chain when I give it a good push.
If I have the bike up and just turning the crank or gently pedaling there is no rubbing, but if I put my weight into it I can see the gear bend out and rub. Happens most on the biggest gear, lessens as I go in on smaller gears, doesn't seem to matter the gear on the back.
Check if the bottom bracket is loose. If the bottom bracket shaft (or axle?) just moves a little in the bottom bracket, the gear can bent outwards. If it is not very loose, you might not notice it without the strong force of your legs.
Similar issue would be if the pedal arm is loose on the shaft.
Edit (answer to comment): when you pull with your hand on the pedal arm, look at the axle. Does it wiggle? It's easier to see on the left side. Then tightening anything usually does not help. You need to open it.
Can someone explain in a comment better how to check it?
If the axle stays still while the pedal arm moves, you need to pull the pedal arm off (special tool needed) and most times you can see at the point where the pedal arm is attached to the axle that the square hole in the arm is not really square anymore.
