Hey Chris633,
Hey, I wrote that article! Thanks so much for referencing it, and I'm glad you liked the idea.
You've pretty much followed the pattern I was thinking of, which is that the power at different proficiency/mastery thresholds should be essentially commensurate with the various levels of item rarity. So, a common or uncommon item is equivalent to the 1st level power of a mastery item. Still, Mastery Items also require attunement, so I think it's fair to give them a little extra something to make them interesting. I really like the ability to bypass immunities and resistances as its situational and also limited in the number of uses. I might have gone for one time a day and scaled it up more slowly, but I was thinking cautiously and trying to maintain balance since I was pitching an idea. I don't think it's necessarily OP.
From there on, the second level of Mastery, achieved at 5th level, should be equivalent to rare items. Items with a +2 bonus are rare, so that's the obvious choice, but I think the 1d6 radiant damage, limited to two uses per day, is quite conservative and wholly appropriate. The next step is tricky since magic item rarity becomes uncoupled from the proficiency thresholds. I'm honestly not sure why they didn't keep to the proficiency thresholds for item powers. Very Rare is the next level, and is appropriate for 11th level or higher characters. That's right in between the 9th and 13th levels where there are proficiency thresholds. My rule of thumb on this was to try to have 3rd stage mastery abilities (gained at 9th level) be a bit weaker than very rare items, or to just give them the +2 bonus at that level, as you have done. I then tended to make up a bit for that with the 4th level of mastery (gained at 13th level). I think giving it 2d6 radiant damage at that point is more than fair. You could certainly have it simply do 1d6 radiant damage on any hit, and it wouldn't be that much more powerful than say a Flame Tongue. That's a rare sword with no pluses, but it does 2d6 fire damage on every hit.
Legendary items are linked to 17th level, which is another proficiency threshold, so Mastery Items should be near equivalents to legendary items at the 5th and final stage of their development. The +3 bonus is a good fit, and the increase in the bypass immunity and resistance power doesn't seem to powerful either. some of those Legendary items are really much more powerful than this sword, but I don't think that's a bad thing at all. This sword has a sense of purpose and character with it's radiant damage and resistance and immunity bypassing. It sounds like a perfect weapon for a paladin or someone with a similar ethos.
That takes me to my last point,in response to Blackwarder's comment. I respectfully disagree, and think it is important to keep the powers thematically linked in a mastery item. One of the best ways to do that is to have powers increase rather than to add whole new powers. That way, the weapon gains a sense of purpose and an identity of its own, which was the whole point of the Legacy Item series - to make items that would scale with the characters as they grew in power and could become signature possessions, part of their character's identity rather than just a collection of interchangeable pluses. It strikes me that your sword does that perfectly.