Spouted portafilters are made to split the flow in 2 whatever is happening in the basket, even with the poorest distribution. The fact that coffee is consistently coming out of the same spout first is actually a sign that it does not come from a poor distribution, otherwise it would sometimes come out of the other spout first.
IMO, you machine is simply not leveled.
Also, you can convince yourself all is going perfectly well inside your spouted portafilter, but the only way to tell is to use a bottomless one. I too was convinced all was great before I started using a bottomless :-)
An old post but I thought I'd add to it - I too was having the same problem of the coffee always extracting out the right side. I put it down to my poor tamping, and even tried tamping deliberately skewed to counter it, but could not solve it and eventually gave up on account of it still tasting good!
Then, last week I randomly descaled my machine due to it becoming increasingly stiff to use, and ever since it's been pouring perfectly evenly! I could only guess reasons for this, but maybe it's worth a try for anyone else having the same issue.
I used this Descaler - "Baby Puly Cleaner - 10 Sachets", available from Happy Donkey amongst other places, and followed these instructions: search youtube for: SCG How-To Guides: Descaling La Pavoni Manual Espresso Machines
Incidentally I don't live in a hard water area, but descaling is still recommended once or twice a year for soft water areas, apparently. It certainly worked wonders for me anyway :-)
A descaled machine is a good thing. However, an uneven flow is almost always the result of either a machine which is out of level, or from some physical issue with the pf and/or spout.
If you remove the basket from the pf, you can see that no matter how unevenly coffee is expressed from the basket into the pf, it drops onto a pf surface which centers it into a cylindrical, small-diameter duct; and that the duct is oriented so that the liquid will fall onto the apex of the double spout's arch and be divided equally into each channel.
That is, the shape of the pf floor, and the egress from the pf, make it almost impossible for anything happening above it to affect the division of the flow.
At a guess, you moved the machine when you descaled it, and serendipitously achieved a better level. Hurray for serendipity.
There are a few things which a barista can read from observing the legs of a pour from a double spout, but an uneven tamp, side-channeling, or the need to descale are not usually among them.
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