We create our own connector for Looker Studio using Google App Script. the connector can show the data without any issue.

but when an editor want to edit the data source, it cant be edited. only the user with the same gmail that can edit the data

I think it should be fixed by changing the permissions of the Apps Script project and granting viewer access to the public

here is the appscript.json file I use

{
  "timeZone": "Asia/Jakarta",
  "dependencies": {},
  "exceptionLogging": "STACKDRIVER",
  "runtimeVersion": "V8",
  "dataStudio": {
    "name": "",
    "logoUrl": "",
    "company": "",
    "companyUrl": "",
    "addonUrl": "",
    "supportUrl": "",
    "description": ""
  },
  "webapp": {
    "access": "ANYONE",
    "executeAs": "USER_ACCESSING"
  }
}