No, if these attacks were meant to inflict the poisoned condition they would specify. For example, the Sprite has an attack that does this:

Shortbow. Ranged Weapon Attack: +6 to hit, range 40/160 ft., one target. Hit: 1 piercing damage, and the target must succeed on a DC 10 Constitution saving throw or become poisoned for 1 minute. If its saving throw result is 5 or lower, the poisoned target falls unconscious for the same duration, or until it takes damage or another creature takes an action to shake it awake.

The Giant Scorpion and the Poisonous Snake don't say anything about the poisoned condition, so they don't inflict it.

First of all the process does not state that it cannot accept its own product as an input. In order for the product not to be a valid input, it would need to specifically exempt it, as it also specifies both that the process works on any poison that comes in doses (not exempted, of course) and that the end product is such a poison.

Next, the ability does state that you need two doses of the same poison. While a case could be made that the base poison and its extra-strong form are the same poison, it seems pretty clear from context and the workings of similar rules that they should not be. So, particularly given your balance concerns, of the two equally RAW interpretations the one differentiating between concentrated and non-concentrated poisons is probably the better choice, especially if Paizo ever publishes a poison variant of the contagion spell.

With outside assistance, there is no maximum limit to the concentration of poison, though the resources required to achieve each level past the soft cap are exponential in growth. Without outside assistance the total time required in minutes is \$2^n - 1\$ where \$n\$ is the desired concentration level of the poison, and the cap is hit when the difference between a level and the previous level is more than 50-60 minutes (depending on GM ruling as to when the dose is used, RAW seems to slightly favor the shorter time limit. We will see later it turns out not to matter, though). This makes the rule:

$$(2^n-1)-(2^{n-1}-1) \le 50$$

or

$$2^n-2^{n-1} \le 50$$

or

$$2^{n-1} \le 50$$

so the cap is at 6, since the 7th level would require 64 minutes of preparation to make, and the 6th level only requires 32. Conveniently, this eliminates any need to resolve our previous ambiguity as to when, exactly, a dose is used.

The 6th level of concentration results in a poison that costs 64 times as much, takes 63 minutes to make and is spoiled by even the slightest interruption, lasts for only an hour itself, and provides a 1039% increase to duration (~11× as long) and +12 to the save DC. This is a fairly expensive option for the meager power it provides, but certainly goes a long way towards making poisons of the less combat oriented type much more viable when used (since you will generally have time to prepare them safely).

Ok, so, for curiosity, I've been trying to optimize the solo crafting order to maximize the highest level of potion created. This is pretty much just a math problem; don't continue reading this unless you are interested:

My best so far is: first hour: get 60 level 1 poisons from 120 level 0 poisons (regular doses)

second hour: get 30 level 2 poisons from 60 level 1 poisons; get 30 level 1 poisons

third hour: get 16 level 3 poisons from 32 level 2 poisons (two of which were crafted at the end of the cycle using produced level 1 poisons), get 30 level 2 poisons from 60 level one poisons (leaving us with 28 left for next time), get 14 level 1 poisons

fourth hour: get 8 level 4 poisons from 16 level 3 poisons, get 14 level 3 poisons, 8 level 2 (one produced from lv 1 poison from this turn), 30 level 1 (28 at end of turn)

fifth hour: 4 level 5 poisons, 8 level 4 poisons (1 produced from threes made this turn), 4 level 3 poisons (leaving 2 for next turn), 15 level 2 poisons, 28 level 1 poisons

sixth hour: 2 level 6 poisons, 4 level 5 poisons, 2 level 4 (1 using poisons produced this turn), 8 level 3 (1 using poisons produced this turn, leaving 6 at end of turn), 14 level 2 (leaving 12 at end of turn), 30 level 1 poisons

seventh hour: 2 level 7 poisons (1 using poisons produced this turn), 2 level 6 poisons (0 at end of turn), 2 level 5 poison, 3 level 4 poisons (1 at end of turn), 6 level 3, 15 level 2, 30 level 1 poisons

eighth hour: 1 level 8 poison, 0 level 7 poison, 1 level 6 poison, 1 level 5 poison (from 1 level 4 produced this turn), 3 level 4 poisons (2 at end of turn), 8 level 3 (1 from 1 level 2 produced this turn, 15 level 2 (14 at end of turn), 30 level 1 poisons.