> During this process, scientists will use a Sun-like star named HD84406 to focus the mirrors

Here is a 1 degree wide view of the neighborhood around HD84406 rendered from Gaia EDR3 data:

https://bsrender.io/sample_renderings/hd84406-1deg-m18-ax100...

Not too many other stars around, and none that are brighter than it within almost a half degree radius. If I zoomed in to the 0.0367 degree FOV of Webb's NirCam instrument, we would only see one other very faint ~21 mag star. However, Webb (and Hubble) can see much fainter stars than Gaia.