If the blue slaad hits you with his claws and you fail the save, what will happen for the PC when they are transformed into a green or red slaad? Will they keep their own personality, or will they become mindless/ a new person? Also what will happen to their stats St Dex Con Int Wis and Cha, HP, and spells known?
RAW: we don't know. "Transformed" isn't a defined term, so we have to infer meaning from context. In the Slaadi context I infer a complete transformation that includes mental stats, abilities, personality, alignment, &c.
As "transform" isn't defined, we've got to look at its uses. Many times in the core set it's used in a context that has no bearing: an arrow transformed into a bolt of lightning, or the transformation described in Wind Walk. Following is a taxonomy of the uses of the term "transform" in the core rulebooks, as applied to characters and creatures with stats/abilities.
Some transformations explicitly do not affect mental abilities, skills, personality, alignment, &c.: druids' wild shape (PHB 66), Shapechange (PHB 275), killing a beast in the Beastlands (DMG 60, optional rule), Cloak of the Bat (DMG 159).
Some transformations change some, but not all of these brain-descriptors: Polymorph and True Polymorph (PHB 266 & 283, change mental stats but not alignment, personality), PC turning into a vampire (MM 296, mental stats don't change, alignment does, and player might even cede control of character to GM—personality change!).
Most transformations, though, don't go into detail: paladins' elder champion and avenging angel (PHB 87 & 88), Animal Shapes (PHB 213), and all of the shapechangers in the MM (doppelganger, lycanthropes, mimic, slaadi, &c.).
(Many more MM entries mention "transformation" in their flavor text, but that's usually in a description of how the monster/race originated, not an action that they take.)
So what about the Slaadi?
The transformation described doesn't specify, but we do have an important bit of context:
Slaadi reproduce by... infecting [humanoids] with a transformative disease called chaos phage.... [By this mechanism] blue slaadi spawn red and green (MM 274).
In context, it must be read that a humanoid succumbing to chaos phage is, in all ways, a slaad.
The only comparable we might have is the Vile Transformation of larva in Hades (DMG 63), which are said to retain "a few faint memories" of their time as humanoids. But there is nothing to indicate that a victim of chaos phage retains even that much.
MM p. 276 under Birth and Transformation states that:
Slaadi reproduce by either implanting humanoid host with eggs or by infecting them with a TRANSFORMATIVE DISEASE called chaos phage.
It then states:
With each transformation, the slaad retains its memories.
Then under Shapechangers states:
Some slaadi can change into the humanoid creatures from which they were originally spawned.
I would think that the chaos phage would be a transformation, therefore the victim would retain his memories and if it was egg based, then no.