This is clearly magic but isn't flagged. As you can see, it's a wand, it has spells. Should be marked magic. If you don't want it to be magic, maybe don't have it be a wand you can use to cast spells actively?

<668hp 522m 641mv 13223tnl (20.92%) 7 AM civilized exam necklace
This necklace of beads is of the sort often carried by religious villagers
of Thera who believe they will help draw the attention of benevolent Gods
to their prayers.

A necklace of prayer beads is a wand, made of gem, and weighs 1 pounds 15 ounces.

<668hp 522m 641mv 13223tnl (20.92%) 7 AM civilized lore necklace
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a necklace of prayer beads can be referred to as 'necklace prayer beads'.
It is worth 1000 copper, and is of the 10th level of power.
It is a wand.
It is made of gem and weighs 1 pounds 15 ounces.
It can be used a maximum of 19 times. It can still be used 10 times.
It contains the spell 'pillar of the heavens' of the 25th level.
When worn, it affects your armor class by -10 points,
your mana by 30 points and your wisdom by 2 points.
It has been imbued with a blessing.
Those with a balanced soul cannot use it.
People of a dark heart cannot use it.
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We have two categories at play here: magic and divine power. This is the latter and will always be a blessed object.

Yeah, that's my point, you guys have split magic and divine. So how can a wand, with spells, be non-magic? I'm not talking about the prog, I'm talking about the actual use of the necklace as a wand, zapping someone. It has spells. Shouldn't it not be able to do that if it's divine and not magic? Keep the prog but lose the magic spells stored within that can be used to zap people like any other magic wand?

The magic/divine divide for objects is based on the source of power, not the means of utilizing that power.

If we wanted to become more distinctive in these categories we could flag these objects slightly differently. We have the ability to have objects commune rather than cast--something I am not sure we have implemented with great consistency--and that might be worth revisiting at some point as well.

I don't see how mage would be able to invoke divine artifacts, and priests/shamans don't have wands skills

...but feel free to debate it on Gameplay.