How to get the Twitter followers count using Twitter API (in 2022)?

Yes, there is a simple way to do this using the Twitter API v2!

The follower and following counts for a user are part of the public_metrics fields in the User object.

The API endpoint and parameters are in the format

https://api.twitter.com/2/users/[ID]?user.fields=public_metrics,[any other fields]

Here's an example of the output, using the twurl command line tool (which handles the authentication etc, you may need to use a library to help with OAuth):

$ twurl -j "/2/users/786491?user.fields=public_metrics,created_at"
{
  "data": {
    "id": "786491",
    "username": "andypiper",
    "created_at": "2007-02-21T15:14:48.000Z",
    "name": "andypiper.xyz",
    "public_metrics": {
      "followers_count": 16570,
      "following_count": 3247,
      "tweet_count": 134651,
      "listed_count": 826
    }
  }
}