The descriptions of the hag eye and soul bag in the MM specifically reference the hags that created the items when talking about who uses the items.
Hag eye:
A hag in the coven can take an action to see what the hag eye sees if the hag eye is on the same plane of existence.
Soul bag:
A soul bag can hold only one evil soul at a time, and only the night hag who crafted the bag can catch a soul with it.
So those items are clearly limited to the hags. But the heartstone, I think, is somewhat open to interpretation.
Heartstone:
This lustrous black gem allows a night hag to become ethereal while it is in her possession. The touch of a heartstone also cures any disease.
From this, it looks like etherealness is only usable by hags, but curing diseases could theoretically work for all.
Jeremy Crawford has commented on this saying it's meant to work only for hags, but DMs can rule otherwise.
If you're looking for a way to use the stone for curing diseases, I'd refer to the 3.5e Wiki, where a heartstone is described as follows:
All night hags carry a periapt known as a heartstone, which instantly cures any disease contracted by the holder. In addition, a heartstone provides a +2 resistance bonus on all saving throws (this bonus is included in the statistics block). A night hag that loses this charm can no longer use etherealness until it can manufacture another (which takes one month). Creatures other than the hag can benefit from the heartstone’s powers, but the periapt shatters after ten uses (any disease cured or saving throw affected counts as a use) and it does not bestow etherealness to a bearer that is not a night hag. If sold, an intact heartstone brings 1,800 gp.
This would be fairly reasonable to use in 5e as well. Naturally, the specifics are down to you as DM. For example, since the saving throws buff is not an official function of the 5e heartstone (according to the MM), you might want to remove that ability from it and adjust the sale price accordingly.
It should be fine, as long as time allows.
Nothing in the rules says that a long rest cannot immediately follow a short rest. In this case, what the characters are doing during those rests are very different.
Indeed, a short rest and a long rest are what many real-life people do before bed: an hour or so of non-strenuous activity, like reading, and then going to sleep. It's not a stretch to say that a D&D character can't spend an hour studying their magical item, and then go to sleep.
The only time where that might be a problem is if the characters don't have the full 9 hours.
Different things are happening during the two rests.
What's really key here is that the activities during the two rests are different. In the short rest portion, the character is studying the magic item, meditating on it, or whatever is required for attunement. In the long rest portion, the character is doing something else, such as sleeping. The attunement process is still active work, just not active relative to adventuring.
I think that this distinction is why attunement is limited to short rests, and why a character should be able to do chain them together.
Best Answer
Can you attune simultaneously? No.
Unfortunately, you are limited to just one item per short rest. The basic rules covers this (emphasis mine):
You can generally attune up to three in total
The Basic Rules covers this (my emphasis):
As long as they aren't the same item, a character can attune to up to 3 items. Your character can definitely attune to both the Cloak of Protection and the Staff of Fire (assuming you also meet the requirements for the Staff).