what I don't get at this point in time is why Rei ever thought he was pathetic and weak, besides bad writing.
I think you underestimate the power of mental (and physical) abuse. It feels like you'd be the type to wonder why abused spouses stay with their abusing partners.
In this case, Rei was initially bought as a slave and has ever had the capacity to cast one spell before collapsing from lack of mana. He was abused and belittled, had few contacts with people outside the team and thus thought himself as a deficient healer. Rei is self-taught, he never had contacts with other healers, never knew that his "heal" was non-standard. And he also thought that he was chosen and bought "for a reason", which let him endure the abuse because of the belief that there was a foundation of trust and sympathy... when he was simply the cheapest white mage slave on the market.
The team also never bothered learning about healers in general. The leader in particular is full of himself and thought of the slave he bought for cheap as a "discount healer", which meant a "deficient healer", which in turn was an opinion supported by his apparent lack of mana. (Though it was actually that Rei's version of the "heal" spell was so powerful that it drained him of his mana in one go. But they wouldn't try to understand that.)
The reason Rei was ranked first among healers is because healers learned about the achievements and hurdles that his team faced. Hearing about cut limbs and lethal injuries being entirely and instantly healed was enough to know that he was way beyond a normal healer's ability. (Though these reports might be questionable, it's enough to put Rei at least tentatively as number 1. It's certainly credible enough when you consider how dangerous the adventurer's life is and how quickly this team rose through the ranks.)
So neither Rei nor his former teammates ever knew about Rei being the #1 healer. One because of isolation and abuse, the others because of arrogance and narrow-mindedness.
I'm not saying this is great writing, but it is not completely unrealistic. Gaslighting works wonder even in real life to undermine someone's self-confidence. Being talented at something is pointless when nobody recognizes your talent and all you hear all the time is how worthless you are. This much at least is more convincing than a majority of other "exiled from party" stories.
(Then again, there is the "exiled in the depths of a deadly dungeon" part, which is as cheap storytelling as many others of these stories.)
