If there would be a probability it should be based on "rarity" (those funky blue/yellow/purple borders")

It's not, we already looked at that, there is no directional correlation between observation frequency and rarity. As an example, 100% coin rain has a rarity of 5 (highest), yet it is one of the most common recipes. It's current probability is at 1.87%, with less than 0.1% chance of it actually being less than 1.38%.

On the other hand, 1 broken shard recipe has a rarity of 1 (most common), yet it is one of the rarest. It's current probability is at 0.64%, with less than 0.1% chance of it actually being above 1.08%. As you can see, it is extremely unlikely that this recipe of rarity 1 has higher chance on occurring than the one with rarity 5. It is even easier to come up with an example where the roles are reversed.

And even if that would be the case I would still be amazed, because if there is a system in place, then why did they even need to add twice the same recipe to the table to improve the odds? they could just as easily gave it a "different rarity" and change the odds for each rarity.

That would have been a lot cleaner and avoided the need for another script to avoid the same recipe to be aviable at the same time. (the double baseplace firefeniks issue the fixed on beta before it came to live)

This is actually easy to explain from implementation perspective. With probabilities, you can't just adjust one of them arbitrarily (as they all need to add up to 1). So it is actually much easier to come up with a pooled system, where you simply specify that recipes in pool 1 are, say, 2.5 time more frequent than recipes in pool 2, and all recipes within the same pool have the same probabilities. Then management of such setup is very simple - you just add/remove recipes as needed into the pools, and actual probabilities are automatically adjusted. So if they have something like that, it is indeed much easier just to add another duplicate recipe to the pool to increase its probability. Otherwise, you'd need to make yet another pool (or several), establish relationships between them etc. That's just more work.