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I try to find the week of the year for Jewish to use it in a global app, which provides general services about the international calendar.
You might try my lib Time4J which offers a Jewish/Hebrew calendar and use following code:
HebrewCalendar hebcal = HebrewCalendar.nowInSystemTime(); int weekOfYear = hebcal.getInt(HebrewCalendar.WEEK_OF_YEAR);
It uses the default week model/definition in Israel which starts the week on Sunday (after Sabbat).
About interoperability with
LocalDate gregorian = hebcal.transform(PlainDate.class).toTemporalAccessor(); HebrewCalendar jewish = PlainDate.from(gregorian).transform(HebrewCalendar.class);