Celestial Method (2014, aka Sora no Method) should have ended at episode 11 Night of the Meteor Shower. Despite hitting the right emotional notes episodes 12 and 13 add very little to a story that was already complete, and may even have damaged it.
The core of Celestial Method is friendships shattered, friendships reborn, and a wish to see friends smile.
Over the first 11 episodes the reasons for Nonoka, Yuzuki, Koharu, Souta and Shione losing their childhood friendships are revealed, resolved, and reconciled.
There is the supernatural element of the saucer in the sky and its childish reification Noel, but Celestial Method is mostly about Nonoka reclaiming her place at the heart of this group of friends.
The focus on friendship in Celestial Method is relentless and it is why the hot springs episode ends up being necessary and entirely devoid of fanservice. The A plot is entirely about reconciling Nonoka and Yuzuki, and the B plot entirely about Noel worming her way into Shione’s heart.
The core story is fully resolved by Night of the Meteor Shower, and I think I would have rated Celestial Method quite highly if it had ended there.
Unfortunately episode 12 Saucerless City veers into It Was All A Dream territory and episode 13 From the Starting Sky has to recover from that. From the Starting Sky does deliver a satisfactory resolution, sort of, but I really question the need for these two episodes to exist at all.
As mentioned at the start of the season Celestial Method is beautifully designed and presented show, and the OP does reflect that:
Celestial Method remains a strong series with some beautiful character work carried by that deep core of friendships restored. However Celestial Method is robbed of greatness by the final two episodes, and ends up as “merely” a good series that is well worth watching at least once.
 Yes, Virigina, there is a plot relevant hot springs episode. 🙂