Your answer is that the UI is natively bollocks in Skyrim. Here's a breakdown of how enchanting works, from what I've observed.
- Selecting an enchantment without selecting a soul gem or an item starts with a base value.
- Selecting an item and then an enchantment applies any modifier from the item (i.e. the bonus from it being Stalhrim or a necklace) but assumes the best soul gem available, or a common soul gem if none is. This is often without applying skill bonuses or potion effects.
- Selecting an enchantment and a soul gem with no item gives you the base value * the modifier from the soul gem used.
- If you aren't using a "lossless soul trap" mod, you can trap a Petty soul in a Grand gem, and that makes it look like you're using a petty gem when scenario #2 happens.
- You don't get your skills applied (usually) until all three components are selected. The same goes for potions.
- Many items seem to have a bellcurved enchanting "cap" that makes it so if your enchanment is 20% stronger, you see the bump clearly, but if it's 80% stronger, it may be minor
- Many enchantments themselves have their own caps. This is particularly true if you have a mod giving unique enchantments or letting you disenchant Daedric items.
- If #7's conditions are met, some enchantments don't change power, and are totally unaffected by your skills
- There are some enchantments that strangely boost each other by a couple of percentage points when combined. This happens because reasonswhynotlorebugswhatever. I don't think it's intended.
- Some enchanments, such as Skein of Magnus from the Archmage Robes, have multiple effects. Only one of those effects is enhanced by the skill. This means an enchantment which "Burns enemies for 10 pts. Enemy Magicka regeneration reduced by 10%" could boost to "Burns enemies for 10 pts, Enemy Magicka reduced by 23%". I think this is tied to the "school of magic" to which the enchantment belongs in the database.
This is all a weakness in the enchanting system; an approach more like classic spellmaking, where you could forge enchantments based on individual effects and materials, would clean this up. As it stands, there's a fair bit of guesswork. One thing that is consistent, however, is that any bonuses which will apply, do apply, when you've picked all three components and are ready to push the button.