When you access another user's Gmail mailbox through Gmail delegation, you may notice that ExtendSync does not appear in the delegated mailbox, even though it is available in your primary mailbox.
Symptoms
ExtendSync appears and loads normally in your primary Gmail mailbox.
When you switch to a delegated mailbox, ExtendSync is not available.
Why This Happens
Google restricts third-party add-ons from running within delegated Gmail accounts for security and privacy reasons.
Because ExtendSync is a third-party Google Workspace add-on, it can run in your primary mailbox but is not available when you access another user's mailbox through Gmail delegation.
This is an expected Google Workspace limitation, not an ExtendSync issue.
What to Expect
ExtendSync can be used from the Gmail mailbox associated with the account where the add-on is installed and authorized.
There is no ExtendSync setting or permission that can enable the add-on within a delegated Gmail mailbox.