(That is an excellent guess and analysis! I really love your reasoning on that, such as with the connection to how the SA2 ghosts were portrayed in Sonic X. That's not the connection that I made but is an excellent idea.
I was actually hinting at the game Sonic Rivals 2, primarily through referencing its Mystic Haunt Zone and Chaotic Inferno Zone.
(Warning: Major Sonic Rivals 2 and Sonic 06 Game/Ending Spoilers Ahead)
The first sentence of my hint referenced how Mystic Haunt Zone is a haunted mansion with paranormal activity present, as well as referencing a main aspect of the plotline wherein the evil supernatural/interdimensional arch villain Ifrit has kidnapped Chao and plans to harm them.
The second sentence speaks more to my headcanon analysis of the relationship between Mystic Haunt Zone and the zone directly after, Chaotic Inferno Zone. In the game, Chaotic Inferno Zone resides in a different dimension, whereas the remainder levels exist in Sonic's world. As it is directly preceded by Mystic Haunt Zone, to me the implication is that the paranormal and anomalous activity taking place in Mystic Haunt Zone is a direct result of the evil entity and energy residing in Chaotic Inferno Zone leaking out of its portal.
The "pseudo-paradoxical" attribute is a reference to another headcanon of mine pertaining to hypothetical relationships between Chaotic Infero Zone from Sonic Rivals 2 and Crisis City from Sonic the Hedgehog (2006). The Rivals series has a fascinating place in Sonic history as it serves as Silver's "debut" following the timeline restructuring event at the conclusion of 06. As Sonic and Elise traveled back in time and snuffed out the flame of Iblis, that entity never came into existence. Therefore, Sonic, Silver and Elise would have never met. Which certainly seems paradoxical, but one can apply multiple theoretical constructs and interpretations to headcanon an explanation such as branching and collapsing timelines.
As Sonic and friends would not consciously remember the events of 06 (although it seems implied that Sonic retains an intrinsic soul-level memory, as one could consider that his soul exists external to the space-time paradigm and retains a record of the experience independent of any particular timeline or associated restructuring events), their first memory of meeting Silver would be in Sonic Rivals, with a later adventure occurring in Sonic Rivals 2.
In Sonic Rivals 2, Chaotic Inferno Zone looks
extremely similar to Crisis City from Sonic 06. Furthermore, Ifrit looks very similar to Iblis from 06. While there is no official in-game explanation for this, my headcanon is that the Ifrit deliberately takes on an appearance for both itself and its pocket dimension to attempt to frighten Silver. This is due to the Ifrit's nature as being an evil, negative entity that feeds on the innocent and utilizes mind control powers. Silver is traditionally depicted as a more naive and innocent character in some ways, but with a tragic past, a strong sense of justice, a heart of courage and a resolve of steel. Furthermore, throughout the story in Rivals 2, Silver seems to be the most aware of and sensitive to the terrible plight that the poor Chao were in (thankfully they ended up being just fine). As a result, one could reasonably headcanon that the Ifrit would have the most interest in targeting, defeating and feeding off of Silver. Given its nature as an interdimensional being, it could potentially be related to Solaris in some way or at least have some knowledge of that entity and events that transpired, and weaponize that information against Silver as, similar to Sonic, he may retain a soul-level intrinsic memory of the event even if it were wiped from conscious memory, and therefore still have the ability to cause deep emotional and spiritual harm.
The last part of the hint referencing "extinguished by the waters of truth" was intended to further hint toward Chaotic Inferno Zone (and subsequently Sonic Rivals 2) by presenting an inverse element (water) associated with the heroes (Silver and friends) in opposition to the element (fire) associated with the arch villain (Ifrit). The reference to deobfuscation was also an oblique hint toward the aforementioned adversarial relationship between Silver and Ifrit.)
[b]Response to your hint
/b]
That is a fantastic hint and was a fun challenge to contemplate. There are many different games that crossed my mind for different reasons, and I'm not fully confident that I have come up with the right answer.
However, my best guess is that you are referencing Sonic CD. Out of everything I considered, the game moment I can think of that your hint reminds me of the most is the legendary race between Sonic and Metal Sonic in Stardust Speedway, Bad Future. As Amy was kidnapped by Metal Sonic back in Collision Chaos, Act 1, Sonic was on a quest to not only defeat Eggman and Metal Sonic, but to rescue Amy. I feel that the "race of a lifetime" and "desperate cries of a girl" fit this scene perfectly. Furthermore, the JP/EUR Soundtrack version of the Stardust Speedway - Bad Future theme uses siren sound effects in the background, which also matches your description. Lastly, I feel "it is time to see who is the real Sonic" perfectly summarizes the archetypal conflict of Sonic and Metal Sonic throughout the history of the
[b]New hint
/b]
Arcs of light soaring through sea and sky shine clear the path of friendship beyond space. Exuberent maritime joy brings new and old friendships alike connected forevermore.