die Beschäftigung
employment
Paid work or a professional activity that someone does.
Er hat nach langer Suche endlich eine neue Beschäftigung gefunden.
After a long search, he finally found new employment.

employment / activity
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employment
Paid work or a professional activity that someone does.
Er hat nach langer Suche endlich eine neue Beschäftigung gefunden.
After a long search, he finally found new employment.

'Beschäftigung' (employment/activity) is a noun derived from the verb 'sich beschäftigen' (to occupy oneself / to engage with something). The ending '-ung' turns the activity into a noun that describes the activity itself or its result.
Womit beschäftigst du dich in deiner Freizeit?
What do you occupy yourself with in your free time?
In the meaning of 'Arbeit' (work) or 'Job' (job), 'Beschäftigung' (employment) is mainly used in formal, official, or economic contexts, for example in employment contracts or statistics.
Er sucht eine geringfügige Beschäftigung für das Wochenende.
He is looking for marginal employment for the weekend.
When referring to a leisure activity, 'Beschäftigung' (activity) is often combined with adjectives like 'sinnvoll' (meaningful), 'kreativ' (creative), or 'entspannend' (relaxing). It can also be referred to as a 'Lieblingsbeschäftigung' (favorite activity).
Gartenarbeit ist für mich eine entspannende Beschäftigung.
Gardening is a relaxing activity for me.
When it is about engaging with a topic, the preposition 'mit' (with) and the dative are almost always used. The pattern is: 'die Beschäftigung mit [Thema]' (engagement with [topic]).
Die Beschäftigung mit der eigenen Vergangenheit kann sehr aufschlussreich sein.
Engagement with one's own past can be very revealing.
work
'die Arbeit' and 'die Beschäftigung' can both mean paid work. In everyday language, 'Arbeit' is the normal word for a job, workplace, or professional activity. 'Beschäftigung' sounds somewhat more formal when it refers to employment, for example in job ads or official texts. In addition, 'Beschäftigung' can also simply mean an activity in one's free time or intensive engagement with a topic. That is why 'Beschäftigung' is broader. If you are talking generally about your job, 'Arbeit' is usually more natural.

Malen ist für viele Kinder eine ruhige Beschäftigung am Nachmittag.
For many children, painting is a quiet activity in the afternoon.
Herr Krüger fährt morgen früh zur Arbeit ins Büro.
Mr. Krüger is going to work at the office early tomorrow morning.