Best is to clean your old bike and relearn how it is supposed to feel. Gritty, bindy, too tight. These are just bad.

BUT, if you insist...you can preload the top cap a little more and that might give you a bit of resistance. To do so, loosen the stem bolts, give another quarter or half turn on the top cap bolt, tighten the stem bolts.

 
Lennard Zinn discussed steering dampers last week:
https://www.velonews.com/...muscle-fibers_493733

That link has a link to a pretty amazing video of one-handed mountsin biking with a damper. It also hadsa link to hopey dampers, which they actually mention for TT/triathlon use too.

Never used it, I would look at geometry first, but could be interesting.

https://www.canecreek.com/product/viscoset/

That Viscoset headset is what you're looking for.

I found that tightening my stem cap did the trick. As long as you don't crank it down super hard, you should be ok. I like having just a little resistance so when I pick up my TT bike, the front wheel doesnt flop all over the place and dent the top tube.

No, it's generally not something you would do without a good reason like a speed wobble. Might be best to get used to a bike that rides correctly, it won't take long.

I used to use a hopey steering damper on my mtb in the late 90's.
Nice product at the time - had a design flaw where the damping knob wouldn't stay at the same position, but I think that's long since been fixed.- probably overtake by changes in bike geometry, suspension, bar and tyre widths on mtbs, but might be interesting on a tri bike to reduce buffeting or stability on rough roads.