The command I've used is /attribute @p minecraft:generic.max_health base set <value>
This command does update the max_health attribute but it does not update the player's health such that it matches the specified max. In other words, I'm able to have a health of 20 while having a max health of 5. Damage is required to update your health value to the correct value. All regeneration heals up to the max_health value.
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That's because it's MAX health, not Health, they are two different things, Max Health is an attribute, Health is an NBT tag.