You cannot cast two leveled spells per turn that way
The ring of spell storing says:
The spell uses the slot level, spell save DC, spell Attack bonus, and Spellcasting Ability of the original caster, but is otherwise treated as if you cast the spell.
Nothing in the description of the ring does it say that an action must be used to cast a spell from the ring. Therefore, "otherwise treated as if you cast the spell" suggests that you need to use an action, bonus action or reaction as appropriate, to cast the spell. This is strictly determined by the requirements of the spell to be cast.
The rules on spells cast as bonus actions state however, that in addition to such a spell, you can only cast a cantrip having a casting time of one action. You cannot, therefore, cast sanctuary (one bonus action) and and beacon of hope (1 action, not a cantrip) on the same turn.
This is a result of the rules for spellcasting, however, nothing caused by the way the spells are cast from the ring.