Tl;dr we need multiple features/mechanics involved in leveling up units such as ascensions every 10 levels, ascensions for each evo stage, artifact + artifact leveling system and add those rewards to places like story mode
Short suggestion, as I don't think I would be able to provide any specific mechanics that would be strictly better than what the devs can create on their own.
Imo there needs to be multiple ways for you to "level up"/"gear up" your units as a way to diversify content and (indirectly/to a lesser extent) make the game less pay to win (as there will be multiple avenues for free to play players to make their units stronger along side whales).
I mainly think of gacha artifact systems when I think of account progression, and while many people hate it, I think it would fit nicely into the overall design of anime td's as one of the MANY ways to progress accounts, and you could perhaps make these artifacts less important to overall power of units like in AA to combat this common complaint.
More on AA, that game had something kind of similar to artifacts with "single set" artifacts that would buff stats, but tying back to what I posted in "Game Mechanic Complexity", there should be something like set bonuses/complex set abilities that require active thinking to make these artifacts stand out from traditional stat boosts.
I also noticed (could be misrembering) that the Haruka sneak had the label "0/3 ascensions" in the unit inspect, which I think would be another great source of content to make account progression feel varied. Again, similar to gacha systems, it would make progression actually feel properly paced if there were multiple "ascension" gates for unit levels/evos (multiple evos would be cool).
All of these different items/artifacts/level up items/ascension items can be placed in story modes and challenges to actually make it WORTH going back to the story and challenges (i personally dont ever touch story ever again after i finish it)