The line 1.e4 c5 2.c3 e6 3.d4 d5 4.exd5 exd5 5.Nf3 may nominally be an Alapin, but it's a type of position that much more closely resembles a French, so I don't think you should take the ECO codes too seriously in this case.

I still do not understand: 1.e4 c5 2.c3 e6 3.d4 d5
A)4.exd5 exd5 5.Nf3 is very likely to transpose to a French Tarrasch; Black very often plays cxd4 anyway.
B)4.e5 is a French Advance Variation; Black can again play cxd4 at a later point.
So it seems to me, that 3...cxd4 4.cxd4 d5 only limits Black's choice, not White's.
Anyone playing the 2.c3 system, will meet 2...e6 in a similar way as he/she meets the French.

I do not understand what the advantage is of
3...cxd4 4.cxd4 d5 compared to 3...d5
immediately.

"Play The 2.c3 Sicilian" by Rozentalis and Harley have this to say about this, "1.e4 c5 2.c3 e6 3.d4 cxd4 4.cxd4 d5 gives White a choice:

a) 5.e5 Nc6 transposes to a form of Advance French where Black has already exchanged on d4.  White might be able to exploit this with 6.Nf3 Qb6 [no mention of 6...Nge7!?] 7.a3 followed by Nc3.

b) With 5.exd5 exd5 White opts for a symmetrical position with slightly better chances; for example: 6.Nc3 Nc6 7.Nge2 Nf6 8.g3 Bg4 9.Bg2 Bb4 10.O-O O-O 11.Bg5 and White has some pressure on the d5-pawn, Palkovi-C.Bauer, Austrian Cht 1999/00."

None of this looks earth shattering though so it certainly looks playable to me.