Pool noodles and pipe insulation foam wraps are pretty much the same stuff -- polyethylene closed cell foam.

We used that stuff as far back as the 1970s for touring bikes and long rides (not races). Looked poofy but was comfy.

Nowadays too much poofy foam can interfere with some brifter operation. In ye olden dayes the brake levers were just brakes, so there was plenty of clearance even with puffy pipe wrap. But it can hinder free movement of integrated brake/shifter levers. So I double wrap or use something like Arundel Synth Gecko.

The double wrap trick is cheap and easy to try. Use an old inner tube, cut into long strips like any bar wrap. Don't worry about accurate or neat trimming because it won't show. The inner tube wrap goes around the bare handlebar. Then finish with your preferred cosmetic overwrap. That thin extra layer of inner tube bar wrap really cuts down on vibration and jolts from rough roads.

There are also gel inserts from Fizik and others. Those go under the bar wrap. But those are expensive for what you get. And the finished wrap will appear uneven and lumpy. Makeshift stuff like double wrap or inner tubes works fine.