Which artifacts are best to equip a hero with?

Why immediately call it a bug? It's a perfectly reasonable mechanic. This happens not only with artifacts but also with skills. For example, if there are two tacticians in the army, the army will only receive bonuses from the one with the higher skill level.

You're right about having multiple tacticians, but not about the artifacts.
This only happens with morale and luck. That is, artifacts that boost morale and luck need to be equipped on the tactician; otherwise, they won't stack with the skill.

Artifacts that boost attack and defense can be equipped on any other hero (one at a time, of course; otherwise, the highest value will be chosen), and they will also stack.
Those who don't believe me, compare the attack/defense values on the map and in battle. ;)

So, for morale/luck, the formula is:
Creature's morale/luck = MAX(SUM(Artifacts) + hero's skill)

For attack/defense:
Creature's attack/defense = MAX(Hero's skill) + MAX(SUM(Artifacts))

Where the maximum is taken for each hero separately.

P.S. By the way, having several tacticians can also be useful. If one is defeated in battle, the bonuses from the second one start to apply. ;) For the same reason, it is recommended to distribute artifacts that boost attack/defense to diversify the risks.