I believe Sirius B is just an exoplanet, and, that the Sirius we see is Sirius + its corona, making it appear much larger than it is. That would place the exoplanet Sirius B at roughly the distance equivalent to Jupiter from our sun. What did not fit with that model is the large proper motion from just the small 50 year barycenter orbit (same as exoplanet orbital period. ) But maybe "stellar aberration" could explain that. I have not analysed this in detail, maybe you are more familiar with the concepts. From the YouTuber you linked to:
The parallel direction of movement of the sun vs Sirius (as binary pair) might cause largest possible effect.