Modern Vespa

Will replacing my 50 year old brake drum improve braking power on the front?

My Vespa barely breaks right now with the front brake and I wonder if my Stoffi shock spring has anything to do with this….

As long as the contact surface of the drum is not glazed up or and the shoes are decent ( may be your problem) the brakes should do their job. Take some 100 grit paper and go over the entire surface to an even scratchiness. I'd do that and put on some nice new shoes, myself.
The spring may allow the front to dive (although, the Stoffi may be stiffer than stock) but won't affect the friction between the shoes and the drum.

Keep the drum. Do the sanding that Moto suggests, to rid it of any glaze and add bite to it.
Buy these two:

https://www.sip-scootershop.com/en/product/brake-shoes-sip-performance-10-front-rear_87330100?q=brake%20sheos%20parformance

https://www.sip-scootershop.com/en/product/cable-brake-front-sip-performance_94180260?q=brake%20sheos%20parformance

That performance cable is the same diameter as any brake cable, but just amazing. Makes a big difference in translating the lever to the brake pads. Really surprised.
The brake pads are softer, so I imagine they will require more scuffing with 80 grit now and then. Small price to pay for the braking power upgrade.

I'm gonna get the cable and brake shoes!

I will say - I did a full hydraulic disc conversion and it was a lot of work. But I'd never look back - it absolutely steam-rolls the drums in breaking power. Especially if you're gonna ride fast in heavy traffic it's a great safety feature. But... costs a lot, no longer OG, and the front of my P2 now looks like a modern PX for the picky.

I'd 2nd starting cheaper and simpler and see if you get to a place where you like the drums well enough for the riding you do

Do both ends, better rear brakes couldn't hurt.

I can lock up both front and rear brakes of my GL with 120/70 11's on them and it has front and rear drums. Just set them up right with good shoes and while it'll still be dive-y, it'll stop you in a hurry when you need it.

Sure, the disc brake is a lot smoother and the front suspension on the older bikes leaves a lot to be desired under hard braking, but that's the fault of the design, not the brakes.