RAW the soul likely ends up in the ring, but you should ignore that
The game has no mechanism to resolve effects that happen at the same time, so the way this is resolved is by ordering them. In this case however, the order does not matter:
Ring first: If the ring gets processed first, the the soul transfers to the ring. The effect of the hut only triggers when the creature dies and the spirit "leaves the body", so it will not pull the spirit out of the ring, as it is not leaving the body any more at that point. The soul would remain in the ring.
Hut first: If the hut gets processed first, then the spirit assumes a spectral form in the border ethereal. Then the ring is processed. The condition of the ring does not care about where your soul is entering the ring from, it just states that if you die, your soul will enter it. So your spirit/soul will enter the ring end cease to be a spectral form. The end result is the same, your soul ends up in the ring.
This is not a very strong case. In particular, it relies on the exact rules text of the hut saying "leaves its body". If the effect was just tied to dying like the ring's, you could order it so that the ring comes first, then the hut. The ring does not stop the soul from leaving it due to other effects (like raise dead), so the hut then would pull the soul back out and turn it into an incorporeal spirit. So absent the "leaves its body" part, it would be entirely RAW to have the spirit/soul end up as a discorporated spectral from.
Normally the order of resolving events that happen at the same time is decided by the DM, unless you are using an optional rule from Xanathar's Guide to Everything (p. 77), then it is decided by the person at the table whose turn it is. As the players are not neccesarily in initative order when they are wiped out by the surprise nova, even if you use the rule, it could be your call.
Focus on the play experience
The more important point is the one you make: what will the play experience be for the player who gets his character stuck in the ring, while to others adventure on? This is much more important than narrow RAW compliance to an edge case situation. You have the power to ignore the rules as the DM, and in particular in a case such as this, where the rules are not really that clear, and where you do it for the benefit of the player's fun, you should.
If you are concerned that the player will feel unfairly treated, you can even give them the choice: let their soul decide if it wants to enter the ring, or if the soul wants to become a spectral form.
Depending on your group's and your play style this also might be a situation where you can step out of in-game, and lay out the options to the player on a meta-level: sit out or play some other character (if available) for the next part of play until they are eventually risen from the dead, or become a spectral form like the others and continue adventuring with them.
PS. The game is vague when it comes to the definition of what a soul is, or what a spirit is, if they are the same, or if they are different things. They mostly seem to be interchangable, but it is not entirely clear and never spelled out explicitly. Conceivably you could even rule that the ring will house your soul, but it is your spirit that becomes a spectral form.
This however might lead to problematic or weird situations that call for lots of more ad-hoc ruling later on, when you end up with the spirit being re-united with the body, and the soul still being stuck in the ring, so I would avoid this.