Get lyrics data from Spotify

I already figured out the URL is https://spclient.wg.spotify.com/color-lyrics/v2/track/${TRACK_ID}?format=json&vocalRemoval=false

And it requires two headers. app-platform: WebPlayer and authorization: Bearer TOKEN.

So using curl I am able to get the lyrics information like that:

$ TRACK_ID=3z8h0TU7ReDPLIbEnYhWZb
$ BEARER_TOKEN=xxxxxxxxxxxxxx
$ curl "https://spclient.wg.spotify.com/color-lyrics/v2/track/${TRACK_ID}?format=json&vocalRemoval=false" -H "app-platform: WebPlayer" -H "authorization: Bearer ${BEARER_TOKEN}"
{
  "lyrics": {
    "syncType": "LINE_SYNCED",
    "lines": [
      {
        "startTimeMs": "110",
        "words": "Is this the real life? Is this just fantasy?",
        "syllables": [],
        "endTimeMs": "0"
      },
      {
        "startTimeMs": "6990",
        "words": "Caught in a landslide, no escape from reality",
        "syllables": [],
        "endTimeMs": "0"
      },
      ...

The actual question is how do I programmatically get the required bearer token? I've tried a token requested using Get Token button on this site: https://developer.spotify.com/console/get-track/

But that token only appears to work for the official API. For the lyrics API I always get the following response for that token:

{
  "error": {
    "status": 403,
    "message": "Client not allowed"
  }
}

Also, the bearer tokens from the link above are way shorter and contain no dashes.

I know I can just copy the Bearer Token that is used by the web client on https://open.spotify.com but the token always expires after a very short amount of time.

So I'm either looking for a manual way to get a permanent token or for a way to programmatically get short-lived tokens.

I'm not looking for a solution in a specific programming language. Any language will do or an abstract explanation.