In case someone has the same issue in the future, this is the solution:
// Inject this
// import com.atlassian.jira.timezone.TimeZoneManager;
DateTimeFormatter formatter = DateTimeFormatter.ofPattern("yyyy-MM-dd HH:mm");
// Get TimeZone of the current logged in user
TimeZone timeZone = timeZoneManager.getLoggedInUserTimeZone();
// Get the user's time
LocalDateTime usersTime = LocalDateTime.now(timeZone.toZoneId())
return formatter.format(usersTime);