Meh. Tradition already has massive perks to growth, and supply scales off that. If supply with tradition really is a problem (I don’t think it is), then just add +2-3

supply to the royal guardhouse
An extra 2-3 units are inconsequential and might as well not even be there. What if the supply scaling off pop was increased for Trad finisher, so that each civ would have anywhere between 7-10 extra supply from pop in late-game compared to a civ that didn't go Trad? After pondering a bit more, I still prefer the initial proposal for consistency; I might've came out of the gate a little to hot with +2, but at +1 supply scaling with era (through 8 eras of the game), that's +8 ships for defense, which is sufficient and reasonable.
I don't think that Tradition needs any buffs. They are doing well and shouldn't be fielding massive armies and navies. There should be a challenge for Tradition and it's managing your smaller supply limit to defend your border.
An extra couple supply introducing itself gradually and incrementally as the game progresses through eras will not allow Trad civs to spontaneously start fielding massive armies / navies out of the blue. Read my prior post; six extra Corvettes / Frigates in Renaissance isn't opening up the flood gates for a conquering spree, but it certainly is enough to help defend a couple coastal cities, while not making you invulnerable. They also have to create/buy these extra units at a slower pace/increased cost compared to a Progress civ. Also, you still wouldn't be able to upgrade these extra ships into Industrial without securing the necessary strategics anyways, so there are still some potential restrictions as to not allow complete freedom.
Giving extra supply to Tradition would make it much more appealing compared to Progress. If that's the wish of Gazebo/community, so be it, but I'm personally against it, as it goes against the flavour of Tradition.
How would it be more appealing? You won't even really notice it in the first few eras as the smaller number will be less impactful, but it'll start to aid as the game progresses. Nobody would look and say, "Hmm, I was going Progress, but now I'm going Trad instead because I'll have +2 supply in Classical". In a scenario where we have 2 civs (1 Trad vs 1 Pro) with 6 cities each, the supply would now slightly favour the Trad civ (if they finish the tree), but adding just one extra city for the Pro civ would make up that difference in supply. Many times the gap will be even wider between city count, and the Pro civ will exceed the Trad's supply. Again, if the Pro civ can't establish a higher city count than the Trad civ, then I've no sympathy because that's lack of execution and your even supply is the result of sub-optimal play, so increase it by widening your empire like Progress civs are supposed to...
I don't want to get too much into this like it's my hill to die on (I didn't even bring this issue up, just figured I'd touch on Stalker's complaint because I see what he's getting at), but the idea came to me and I figured I'd throw it out there. Quite frankly, I think it's a good one, and as explained in my initial post, would even bring a new element into the game regarding Trad vassals that have no shot of ever liberating themselves in the current system -- I find Trad civs tend to generally be conquered easier (aside from the capital) than others due to their (usually) peaceful intentions and obvious supply disadvantage.