You should have the contact of HR. Doesn't hurt to drop them an email / whataspp to check if you hadn't already done so in the past 3 - 4 weeks.

The waiting is painful (from personal experience). But as another poster mentioned, there are still a few checks to do between the verbal and official offer, so that 3 - 4 weeks waiting time is quite expected.

With the verbal offer, things are 99% confirmed, so just hang in there!