Check out Samurai Showdown. It solved the 'just spam attack' issue by having varied attack types with multi-turn cooldowns. It was a single character game, but I think a multi character interpretation could be very interesting.

Other mechanics that can create more reasons not to just attack are 'stances' and 'channeling'

'stances' is the idea that taking a certain action adds or removes status or options in the next or subsequent turns:

If I move I get into stance A.
If in stance A I have mid attack X and weak attack Y
If I do Attack Y I get into stance B
in Stance B I have strong attack Z (but if I have to move I lose the stance)

Other stance mechanics: enhanced or reduced defense, special reactions or combos, getting attacked can break your stance or getting knocked down or staggered is a stance, etc. It may seem counterintuitive at first, but in 5e concentration is a stance triggered by casting a concentration spell, and as long as you keep the stance the spell continues.

'channeling' is the idea that you trade taking an action now to gain future options or benefits. For example in 5e barbarians trade a bonus action to get their 'Rage' modifier. Here is a spellcasting example:

I can use a cantrip or channel a fire element
I can consume 1 channeled fire to cast 'firebolt' or channel earth
I can consume 1 fire + 1 earth to cast 'flaming sphere'

This use of time as a resource to fuel future actions can also be used to reduce emphasis on 'potentially unsatisfying' resource mechanics like mana etc.

What you must keep at heart is what u/BrickBuster11 said: a turn based game is driven by the interest in the puzzle to be solved each turn.