I just thought of another question about item skills, albeit not about stacking.
If there is an item skill that shares a name with a Mastery skill (for example, Doom Bolt), and you have +X to Doom Bolt, would that affect the level of the item skill, or just the level of the Mastery skill?
It’s a separate Doombolt, so it doesn’t affect the Doombolt in the Occultist mastery. Items with skills from masteries usually have a set level (it says which level in the description).
Game consider it two different skills (and the stats are actually a bit different, iirc Doom Bolt on gear has 1.5 m radius, and Doom Bolt from Occultist skill tree has 2.5). Or, rather, one is castable skill you can bind devotions to, and other is just a proc, with fixed damage values. You can, usually, get a higher-leveled gear with higher-leveled version of affix that grants proc, that gives it more base damage, there are several tiers for each affix.