Modern Vespa

It feels as if some slight brake pressure is being applied to the rear wheel.
How do I check if this is so? And how do I fix it?
If it's not the brake then what else could it be?

Thanks,
Dani

Put it on the centerstand and spin the rear wheel with your hand. See if you feel any abnormal resistance.

When on the center stand there is definitely some resistance, but when starting cold the rear wheel still spins. Which make me think it may not necessarily be the brakes.

Do you think overinflated tires can cause this syndrome?

There is going to be a little resistance due to the belt for the CVT. If the wheel is spinning by itself when the engine is running, you probably don't have any brake drag. If you don't see or hear anything scraping, it's probably nothing. What makes you think that there's pressure being applied to the rear wheel? No, I don't think it's your tires being over-inflated. But, are they?

So that rules out the brakes. The only reason i ask this is because the Vespa Shop recently adjusted my breaks so that I didn't have to compress the left brake handle so much There is definitely more drag on the rear wheel when I try to push the bike with my legs. No idea.... just a mindless thought that went through my head

If your rear brake is a DRUM brake and since you recently had them adjusted, then it could possibly be dragging very slightly if you're feeling a noticeable difference. If you have a disc brake on the rear, there is nothing they could have done to cause this.
If you have a drum brake, there will be an adjustment nut near the brake that you can turn to the left to release the engagement point. Like I said, I don't know which type of brake you have on your scooter.

When using scoot the engine casing/wheel/hub get very hot and the brakes expand with heat and can bind on if over adjusted when cold
For this reason I adjust the rear brake so it's just away from drum when hot

It's already been answered, I know, but just FYI:

Over-inflated tires = less rolling resistance

Under-inflated tires = higher rolling resistance, and would be harder to push (but really only if nearly flat).

Have you ever had to push a car in neutral? Now think about doing the same task with all 4 tires flat - under-inflation to the extreme - doesn't sound fun, does it?