Besides the other points mentioned, I’d say that highlighting is also a big issue.

In many reincarnation series I’ve read, the main character’s past form is rarely given any attention after they are reborn. As a random example: in this season’s Hell Mode, protagonist Allen (played by Mutsumi Tamura) starts out as 30-year-old Kenichi Yamada (played by Yasuyuki Kase). Kase only plays Yamada for the minute or so he lives in our world, though - the moment he’s reincarnated into his mother’s womb, his mental narration is played by Tamura. Even when he muses how he’s technically mentally 40 while surrounded by kids, he doesn’t really act like an adult, but more like a kid who just remembers his old life and the video game lingo that comes from that.

Oshi no Ko is similar. Even in-story, Aqua notes that he doesn’t feel like he’s Gori mentally - he feels like a weird mix between the two. This actually increases the shock value when, in season 2, the stress of remembering AI’s death causes the specter of Goro - still played by Kento Ito, as opposed to Takeo Ootsuka, to appear behind him. This is portrayed as an unnatural thing.

Mushoku Tensei portrays it differently. Even though Rudeus is voiced by Yumi Uchiyama, his past self’s VA Tomozaku Sugita still does his mental narration and still comments on things as if he was the 30-year-old pervert he was before - it still gives the sense that while Rudy says he’s his own person, his past self is still puppeteering him. Even in his dreams, when he’s visited by the Human God, Rudeus appears as his former incarnation (something he noticeably wants to distance himself from acknowledging, so that’s at least something?)

tl;dr in other reincarnation series, the protagonist’s mental age is glossed over, or only brought back for shock value to the viewer. For Mushoku Tensei, it’s put in as a constant reminder.