On android, urlcheck is a great app to modify URLs before sharing or opening. For this problem, you can use the json editor, and add the following two entries with small a regex I wrote:

  "shorten Youtube": {
    "regex": "^https?:\/\/(?:[a-z0-9-]+\\.)*?youtube\\.com\/(.*)&.*",
    "replacement": [
      "https:\/\/youtube.com\/$1"
    ],
    "enabled": true
  },
  "shorten Youtu.be": {
    "regex": "^https?:\/\/(?:[a-z0-9-]+\\.)*?youtu\\.be\/([^?]*)?.*",
    "replacement": [
      "https:\/\/youtube.com\/watch?v=$1"
    ],
    "enabled": true
  },

A button to shorten the link appears in urkcheck when the pattern matches. You can all auto shorten them by replacing “enabled”: true
With
“automatic”: true