[Request] Change to "Connect to Google Vertex" AI docs

[dhru42]

Description

Need to make a change to verbiage informing users that they need to enter API key when there isn't an API key to be entered.

Generate an API Key -> Generate a KEY

it's not really an API Key
Under Authentication, enter your API key.
=> enter your Credentials JSON

Background & resources

Discussion: https://elastic.slack.com/archives/C056H3WA1BL/p1738794006321069

Which documentation set does this change impact?

ESS and serverless

ESS release

N/A

Serverless release

TBD

Feature differences

change to documentation

API docs impact

N/A

Prerequisites, privileges, feature flags

N/A