The best strategy games like ActRaiser are ActRaiser Renaissance, SolSeraph and Populous. Below are 5, each with the reason it is here — and, at the end, what filtering to strategy costs you.
Filtering to strategy means you want to be making decisions rather than executing them. It is the right filter when what you liked was the planning.
What you get: Losing that teaches you something. A good strategy game makes the reason you lost legible, so the next attempt is different rather than just longer.
What made ActRaiser worth playing in the first place is covered on the full list. This page is the strategy part of that answer, and only the strategy part.
The remake, with the simulation half considerably expanded.
Made explicitly as an ActRaiser successor.
If the god-game half was the appeal.
Indirect kingdom management where you cannot control the heroes.
Building a kingdom and leading it into battle, and charming.
Pace and immediacy. Strategy games are slow by design, and the good ones expect you to sit with a screen for a while before anything happens.
Specifically, these are strong answers for ActRaiser that are not strategy games, so they are not on this page:
The full list is on games like ActRaiser — 9 picks, no genre filter.
ActRaiser Renaissance. The remake, with the simulation half considerably expanded.
No. ActRaiser released on the Super Nintendo, but a recommendation is only useful if you can play it, so the picks above span platforms and eras. What they share is the genre and the reason.
Scale. Tactics is one battle, unit by unit. Strategy is the campaign around it — economy, territory, and which battles to fight at all.
Turn-based ones, yes; the genre started on consoles. Real-time strategy is genuinely worse without a mouse, with a handful of exceptions built for the pad.
By hand. Each pick was written for the full ActRaiser list first, on what the game actually does, and this page is the part of that list that is strategy — never a genre tag lookup, which is how "best racing games like Super Mario 64" used to be a page on this site.
Or read the strategy guide for where to start in the genre generally.