In the Scheveningen structure shown the purpose of the d6-d5 break is twofold. First, to attack White's e-pawn and second, to free Black's dark squared Bishop which is usually passively placed on e7. Once free that Bishop can pin White's c3 Knight or find a strong square on c5.
Idea behind Sicilian d6-d5 break

I’m not sure if your diagram is correct?
The d5 break is a thematic idea to liberate the position for black. With that said, you don’t take it literally because there is place and time for it, in other cases, d5 can be a weakening move or blunder.
d6 fights for e5 allowing you Nf6. In e6 Sicilians, we don’t have d6 to fight for the e5 square so we use other resources like Qc2 or Nf6 and have further options of f5 as the break and d7 becomes the base of the pawn chain.
In the Alapin and McDonnell Attack, 2.d5 is a book and strong move.
In the Katalimov, d5 or d6 takes heavy consideration as it exposes blacks king.
Just brain storming…

Thanks for the answers, both of the answers make sense and mention what i feel during a game:
1. d6 preventing(somewhat) white from dislodging my knight
2. Freeing my pieces
But the crazy thing is , by the time tension around center is resolved, the game more or less has already been decided.
What I am saying is the whole game somewhat revolves around the resolution in the center, by the time my pieces are free because of d6 getting exchanged or d5 I have already won or lost.
Maybe its just a characteristic of non-perfect or bad play.

It’s hard to say, if you are playing d6 Sicilian, you’re going for a complex game and a transposition you enjoy; a Najdorf, Dragon/dorf , Schevenigian and Opencensky. All the middle game plans and ideas associated with it.
Too much stuff for me to figure out in a rapid game, so I switched to e6 Sicilians for simplicity but had to learn how to deal with dark square weaknesses, e5 being one off the them.
With pawns on e6 and d6 Black frequently has to play e5 before he can think of d5 and that takes time. I remember the late GM Walter Browne saying "If you have to play e5 anyway why not do it in one move?" (via the Najdorf). That quote actually got me to switch because I was getting crushed on the K-Side before I could do anything in the center which sounds like your problem.

We are no experts....ask an IM or GM in their YouTube,twitch chat
No, we are not experts but a little knowledge is enough to be dangerous at the advanced club level.
Understanding strategy and counter play is what all Sicilian variations are for.
As an example, the e5 lines in the Sicilian offer counter play strategy at the expense of giving up holes for white’s knights and a backward d6 pawn but black has resources and plans for the concession.
What should be the plan after achieving the d6-d5 push in Sicilian structure?
Is it to enter endgame and convert the pawn majority in the center?
Why d6-d5 is one of the themes of sicilian structure? I always find d6 helpful in fighting white's king-side push.
Thanks