How to animate drawing a wide strip on a plane?

I’m not sure I’ve grasped your problem correctly. But maybe the following will help

Create a curved plane surface which dynamically changes its size

From the Collection of examples from discourse.threejs.org
https://hofk.de/main/discourse.threejs/2019/RoadRace/RoadRace.html

See also Addon to create special / extended geometries

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