In the answer to this question, it's clear that RAW, short rests cannot occurring during a long rest; you have to choose which before you begin.
This question confirms that you can cast spells before the end of a long rest.
The catnap spell description (Xanathar's Guide to Everything, p. 151) states:
You make a calming gesture, and up to three willing creatures of your choice that you can see within range fall unconscious for the spell's duration. The spell ends on a target early if it takes damage or someone uses an action to shake or slap it awake. If a target remains unconscious for the full duration, that target gains the benefit of a short rest, and it can't be affected by this spell again until it finishes a long rest.
Errata has confirmed that a long rest requires at least 6 hours of sleep. so…
Can I circumvent this short rest/long rest exclusivity by casting catnap on my party members and myself before conking out for the full long rest duration?
Best Answer
Certainly, you could use catnap during (or right before) a long rest
You certainly could gain the benefits of a short rest "during" a long rest by casting this spell during a long rest. Nothing in the spell's description suggests that you can not use it during a long rest, and nothing in the spell's description that would cause a long rest to end while it was in effect.
A more likely scenario is that you would use this spell before you begin a long rest (or at the very start), so that you could have the benefits of a short rest in 10 minutes, and then be prepared to use those benefits if your long rest is interrupted (e.g. you're attacked two hours in). Using catnap in the middle of a long rest seems to have few possible benefits compared to that.
A 3rd level spell slot is a heavy price to pay for this strategy, and many characters will find that such a spell slot would be more valuable than the benefits of a short rest. Also note that some DMs will permit you to gain the benefits of a short rest if your long rest is rudely interrupted (say, by an ambush) more than an hour into it. Amongst those DMs is Jeremy Crawford, lead designer of the game.
But if you are in an area where you think your rest may be interrupted very early on, and have many characters who benefit highly from short rests, by all means employ this strategy.