I believe your goal is as follows.

• You want to retrieve the signature of Gmail as follows. The image is from your question.

  

• You want to achieve this using googleapis for Node.js.

In this case, how about the following sample script?

Sample script 1:

Please use auth in your script. This sample script uses the method of users.settings.sendAs.list.

const gmail = google.gmail({ version: "v1", auth });
const res1 = await gmail.users.settings.sendAs.list({ userId: "me" }).catch((err) => console.log(err));
if (!res1) return;
console.log(res1.data);

Sample script 2:

Please use auth in your script. This sample script uses the method of users.settings.sendAs.get .

const gmail = google.gmail({ version: "v1", auth });
const res2 = await gmail.users.settings.sendAs.get({ userId: "me", sendAsEmail: "### your Email address ###" }).catch((err) => console.log(err));
if (!res2) return;
console.log(res2.data);

Note:

• This answer supposes that you have already been able to get values from Gmail using Gmail API. Please be careful about this.

References:

• Method: users.settings.sendAs.list
• Method: users.settings.sendAs.get
• Node.js quickstart for Gmail API
• google-api-nodejs-client