I picked up the sport badminton living here in Hong Kong and I love it! The easiest way that I have found to find a group to play is via the meetup app. You can create an account on meetup.com and search badminton and there are at least a dozen groups.
There is an admin/host who will book the courts and provide the shuttles and ask each person to pay, it's around $60 or so depending on how many people participate (check the specific meetup for costs and court details).
Personally I'm in HK Happy Badminton Group. They have courts booked DAILY separated by level: Advanced Beginner, Lower Intermediate, and Intermediate.
It's a quick way to meet lots of people participating in this great sport! Just note the spots fill up fast, so it's better to find a day 7-10 days in advance and sign up. You can PM me if you want to join the whatsapp group as they post any openings for sessions coming up in the next day or so.
I suggest joining a few badminton meetup groups just to try out different areas, groups, and increase your chances to find the timings, courts, dates that are most suitable for you.
I hope you get to play soon!!