Looking at the bike it looks like it’s spent time in a damp environment.
I’d suggest your main problem is a lack of lubrication, or corrosion, in the brake cam pivot shafts. The brake plate needs to be completely dismantled, cleaned out and the moving parts lubricated with a suitable brake grease.
The cable also looks completely dry and needs some oil but I don’t think that’s the main problem so unless it’s frayed I don’t see that a heavy duty one will fix anything.
Finally, the angle of the brake operating arms isn’t as good as it could be. You will have noticed that almost all of the cable adjustment has been taken up (you are NOT missing an adjuster at the handlebar end btw, that is as per design). The brake arms are held onto the brake cam pivot shafts by a nut and a spring washer and located on splines. If you remove the arms they can be rotated clockwise by a spline or two. This will allow the adjuster to be backed off and it will give the arms the best mechanical advantage as you apply the brake. Your arms have gone “past” a 90 degree angle with the end of the inner cable, so as you pull harder you are actually getting less mechanical advantage.
However, you do need to confirm that the brake shoes aren’t badly worn away before doing this. Obviously, if they are they need replacing because this could be the cause of the loss of adjustment. If they still have enough thickness, rotating the arms on their shafts will help give you a more powerful brake.
I often post the photo below, of my own bike, showing how the brake arms SHOULD be positioned when the brake is hard on, because this is a common issue, even on bikes coming straight from a dealer.