Izuku in Mushoku Tensei

Izuku, after losing everyone he loves, defeating all evil not just in Japan, but the entire world, dies at the age of 32. after all the deeds he has done he was allowed to have a second chance at life, either with his memories or not (not telling you now).
He was Reincarnated into an anime we all know and probably don't exactly love, but don't hate either, Mushoku Tensei!

(This Izuku has a different personality btw)
This fanfic has the world, monsters and people of Mushoku Tensei,
The mechanics like a mana core of TBATE(e.g. you start of with no mana core then when you awaken you go to black then dark red, solid red and then light red, this happens for every colour- red, orange, yellow, silver, white and maybe even further?

I Do own this specific story, but not MHA, TBATE, or Mushoku Tensei, keep that in mind.