What I've done is, if you select an enemy unit to attack, the player's unit marks that enemy, and simply moves towards the tile the enemy is on. Part of the logic in the player's unit should be CanAttack(), meaning, is it close enough to attack. So, while you're target tile is the one the enemy is standing on, your unit will stop once it's in attack range (a few tiles for ranged units, adjacent tile for melee unit).

If your enemy target moves, yes, you have to recalculate, but you should always use the CanAttack() to over-ride whether your unit has reached its intended tile or not to stop moving and start attacking.

ok but the tile the target is currently standing on is not walkable (and not "pathfindable") though since its blocked by the target unit itself. Maybe make an exception for that specific tile...

But basically this is how its done?

I think that's flawed. You should be able to select any walkable tile for pathfinding, whether a unit (enemy or friendly unit) is on it or not.

If you select a tile a friendly unit is on, the tile is the destination; if the friendly unit doesn't move, then your unit will stop when it gets as close as it can to that tile. If the friendly unit does move, then you will walk onto the tile as if the friendly unit was never there.

If you select a tile an enemy unit is on, then the enemy unit is the destination, and your pathfinding may have to be updated if that unit moves.