This is often called "the slippery slope of knock-on upgrades" which can get expensive quickly.
There are two simple and relatively cheap upgrades to try.
Replace the brake pad inserts with modern compound Kool Stop. They will brake better than the original ones, which may also be a bit hardened with age. There will be a model that fits your brake pad holders. A relatively invisible upgrade.
Replace the bartape with something a bit nicer. I think you've got the thin nylon strap stuff, and its come away from the corners. Try some new modern material/retro style. You might choose to remain with white to match the brake levers, or a more dirt-hiding black to match the saddle, or some other colour that appeals. But wrap it properly and it will be more comfortable.
If you change the wheels to get aluminium braking track rims, then the brakes may not reach - modern wheels are 622mm and yours are probably 630mm or maybe 635mm. This would mean new brakes, which may mean new brake levers as well as new tyres and tubes. See how the knock-on effect works ?
Other option is to sell it on and buy a more modern bike. Someone would love to own that loverly `80s beauty.