What are the uses of the Golden Apple?

Normally, the apple is valuable in combat as an 'oh no' button. I have found 3 uses so far aside from the obvious one, which all give permanent benefits. That means using it in combat is typically a 'last resort'. You would want to use the healing potions, which do the same thing worse (heal 12 instead of 25 hp), first.

1. Scroll of Midas

If you have a Scroll of Midas, you can use it on a Golden Apple to gain money. Unfortunately the reward is rather small at only 300 coins. For comparison, a regular purple item rewards you with 1,800 coins. I don't recommend ever doing this.

2. Enchant at a library

Attempting to enchant a regular consumable at a library will simply fail; the library won't accept the item. The golden apple, however, if enchanted is consumed and produces one of Lucy's rare skills.

These are typically highly valuable swift skills that tend to strictly increase the power of the deck, with more powerful ones unlockable at the Research center with Time Shade.

Because you are usually restricted to 1 such skill, having an additional one is very valuable. This is my preferred use of the apple.

3. Use at the smithy

The Golden apple can be used at a smithy in place of a regular item as a 'joker'. It is most valuable in place of a purple item, to create a maximum-quality orange item from another purple item.

This is situationally how I use my apple, as there are some purple items that aren't very valuable. This can happen if:

3a. I have many items that do the same thing; superfluous items.

For example: As each character has only 2 slots, and there is typically one 'healing' character, the third healing item is superfluous.

3b. There's a purple item I'd rather not use.

A good example is Vadzerald, especially early game. The cost of gradually making my cards unplayable is not worth the reward of 20% increased power or so.

Strategy summary

If you obtain an apple, try to save it. Check if you have useless purple items (or 2 useless blue items). If so, use it at the smithy as a purple item. Otherwise, use it at the library to gain a valuable support skill. If neither is available to you and you're already in stage 5, just use it as a healing potion.