I don't see your pictures but few my observations:
Stats from enforcements to Personalized jewellery placed on augment appear to be ignored, but i tested mine with Stamina ones only.
I usually unequp/equip gear and/or re-summon companion, it happens the changes are stuck somewhere in abyss and ignored till you forcibly refresh it.
In case of non-augment companion, pet % enh stone worked correctly only with first (from top) defensive slot. Maybe it was effect of 2 slotted bonding stones or companion-specific.
Some gear gives lower stats when placed on augment companion, like ring from Dragonborn pack.
It's correct that gear score is not affected by companion stats, although it does appear that the item enchantments are not being taken into account - certainly not the defense ones at least - see how there is no defense or deflect listed? I'm almost positive that mine on my Black Dragon stone are included, unless something has changed or there's a new bug (I'm at work, so can't check that right now).
Hp does add GS, if you have it in an augment. Not sure if it is due to a + max hp feat on the actual character, though because it only adds a tiny amount of GS.
Hp does add GS, if you have it in an augment. But no other stats do. Not sure if it is due to a + max hp feat on the actual character, though because it only adds a tiny amount of GS.
Your assumption is correct. Also if your pet does not normally have stats (AP) then those gems will not transfer, but if it does have the stat (regen) then they will transfer.
Comments
Stats from enforcements to Personalized jewellery placed on augment appear to be ignored, but i tested mine with Stamina ones only.
I usually unequp/equip gear and/or re-summon companion, it happens the changes are stuck somewhere in abyss and ignored till you forcibly refresh it.
In case of non-augment companion, pet % enh stone worked correctly only with first (from top) defensive slot. Maybe it was effect of 2 slotted bonding stones or companion-specific.
Some gear gives lower stats when placed on augment companion, like ring from Dragonborn pack.
— (The unwritten rule)
Correct: your stats will increase by the augment pet's stats, but your GS will not increase.
Hp does add GS, if you have it in an augment. Not sure if it is due to a + max hp feat on the actual character, though because it only adds a tiny amount of GS.
Your assumption is correct. Also if your pet does not normally have stats (AP) then those gems will not transfer, but if it does have the stat (regen) then they will transfer.