It sounds like problem is in electrical system not the bulb, since new bulb didn't fix it.
I have had a similar problem as yours going on on my 2002 1.8T for quite sometimes.
...dim headlights, horn not so loud, melted 150A fuse & fuse block on top of battery, and some power loss...
After days of analysis, the problem was fixed with the cost of one fuse and a piece of sand paper.
I removed the big black wire on the far left of fuse block on top of battery,
used metal sand paper to clean oxidized contact surface on its terminal,
and put it back with a new 150A fuse, tighten it very tightly.
Once electrical current flows well, all problems above were solved with a bonus of a little better gas mileage.
It's been two weeks now and everything is still looking good.
I was lucky it's not something bigger and costlier.
Hope this might help. Good luck.