落ち着く: becoming calmer and everyday life settling down
Distinguish becoming a little calmer after a deep breath from life finally settling after moving boxes are put away. Read the subject, degree, and circumstances of each change.
The degree of calm in 少し落ち着いた
落ち着く (おちつく) can describe becoming calmer or settling into a stable state. In 「深く息を吸うと少し落ち着いた。」, the speaker became a little calmer after taking a deep breath.
「少し」 limits the degree of that change. Saying that all anxiety disappeared or that the speaker became completely peaceful would lose the original statement that the speaker calmed down only a little.
What settles in 生活が落ち着く?
In 「引っ越しの荷物が片付き、生活がようやく落ち着く。」, life is finally settling down with the moving boxes put away. The subject is 「生活」, so a translation that mentions only an improved mood misses the settling of everyday life.
「荷物が片付き」 gives the state of the moving belongings, while 「ようやく」 marks the eventual settling of life. The nonpast 「落ち着く」 does not report that every moving preparation was already completed or that all everyday problems were resolved.
Read the subject, degree, and circumstances together
For the breathing example, attend to the speaker's change and 「少し」; for the moving example, attend to everyday life and 「ようやく」. The same verb concerns different things becoming calmer or more stable in different circumstances.
The put-away boxes help explain the context in which life settles down. That settling is more than a report about the boxes alone, and it should not be collapsed with emotional calm into the single idea of feeling happier.
Can 「生活がようやく落ち着く」 be translated as the speaker becoming completely at ease?
Show the answer and why
That changes what the sentence describes. Its subject is everyday life, which is finally settling after the moving belongings are put away. Complete emotional peace and the resolution of every problem are not stated.