There's like pros and cons to each method.

Pros for short story:

I've already completed 1 and a half stories in this format

Much more lore can be inserted into them

Fits how the four characters (Marina, Skye, Arcanica and Parsley) were fated to meet more clearly

Cons for short story:

It is essentially 360 pages of required reading for a 600+ page story that's already a hard sell to begin with

Focusing on a singular character causes the prose of the stories to be one-track minded asides a few lore-dumps

Pros for integrated backgrounds:

Can (possibly) feel more natural (if done properly)

Lower barrier of entry for the main plot

Retention of information pertinent to their backstory will be greater as it was plot relevant in the moment

Cons for integrated backgrounds:

Will likely bloat the main work by another 200ish pages

Many important pieces of lore may need to be cut thanks to just not being relevant to the context of the character reminiscing on their history