How exactly does "stability" work in analytical anion groups from qualitative analysis?

(Just a heads up, I'm painfully aware of how obnoxiously long this is, Sorry about that!)

What exactly does stability of the group reagent (dil HCl, conc H2SO4, BaCl2, etc..) mean in this context?

To quote my textbook exactly (this is highschool-level chem by the way, but feel free to add more details as long as the explanation itself has that in mind): "Hydrochloric acid is more stable than the acids from which the group anions are derived, so when it reacts with these anions salts, it replaces the less stable acids which are easy to volatilize or decompose in the form of gases which can be detected by suitable reagents "

Is it an inherent property of any reagent in isolation, which is then compared to the required anions' acids (at least for groups whose reagent is an acid) to determine the suitable reagent for each group (As in Kc of the reagent and the produced acid are orders of magnitudes apart that the reagent's anions are undetectable?, but that wouldn't really make sense considering HCl and H2SO4 are strong acids dissociation-wise), So if all we cared about was that the reagents don't dissociate much relative to the products (ppt./volatile gas), considering strong acids would be borderline stupid.

Is it a property that is fundementally dependent on the ions in question, as in that it's defined as being "with respect to" said anion rather than "more stable than" it in some universal sense? (At least for when the group reagent is a specific salt (BaCl2, for example), is it that the salt's cation really "wants" to bond with its group anions, beacuse that chemical releases a significant amount energy when formed which is what stability normally means, but then again, what about strong acids?)

Is it more nuanced than this? Is it a blend of these views?

Also is it different depending on whether the reagent is an acid, a salt, an acidified other type of chemical, or something else? I mean, they are different chemicals and it would make sense that they get different treatments when deciding what reagent works for what, but then again, I have no idea what stability means in this context so I'm probably being unnecessarily verbose because I'm missing something pretty simple.

Bonus Question: Why do we use Dilute HCl in one group, but Concentrated H2SO4 in another? Is it because conc H2SO4 prevents haloacids from dissolving, rather than evolving to be detected, when detecting halogen ions?