docs(protocol): restore the success gate on terminal auth reconnect (#2623)

* docs(protocol): restore the success gate on terminal auth reconnect

* docs(protocol): allow retrying terminal auth on the existing connection first

Author: benbrandt

docs/protocol/v1/authentication.mdx

@@ -177,7 +177,7 @@ For a `terminal` method, the Client:
 3. Presents the terminal to the user and waits for the process to exit. Exit
    status zero signals success; a non-zero status, termination without an exit
    status, or cancellation signals failure.
-4. Reconnects and reinitializes the ACP Agent.
+4. On success, reconnects and reinitializes the ACP Agent.
 
 The descriptor cannot provide a command. The Client derives the command from its
 own Agent configuration. Agents **SHOULD** provide arguments that enter a

docs/protocol/v1/draft/authentication.mdx

@@ -177,7 +177,7 @@ For a `terminal` method, the Client:
 3. Presents the terminal to the user and waits for the process to exit. Exit
    status zero signals success; a non-zero status, termination without an exit
    status, or cancellation signals failure.
-4. Reconnects and reinitializes the ACP Agent.
+4. On success, reconnects and reinitializes the ACP Agent.
 
 The descriptor cannot provide a command. The Client derives the command from its
 own Agent configuration. Agents **SHOULD** provide arguments that enter a

docs/protocol/v2/authentication.mdx

@@ -206,8 +206,7 @@ For a `terminal` method, the Client:
 3. Presents the terminal to the user and waits for the process to exit. Exit
    status zero signals success; a non-zero status, termination without an exit
    status, or cancellation signals failure.
-4. Reconnects and reinitializes the ACP Agent, then retries an operation rejected
-   for requiring authentication. For an already-inserted prompt, see
+4. On success, retries an operation rejected for requiring authentication. The Client **SHOULD** first close the existing ACP connection, start and initialize a new one, and resume with `session/resume` any sessions it wants to keep, since the running Agent may not pick up the new credentials. It **MAY** instead retry on the existing connection first, and reconnect only if the retry still fails with `auth_required`. For an already-inserted prompt, see
    [Authentication failures during session work](#authentication-failures-during-session-work).
 
 The descriptor cannot provide a command. The Client derives the command from its

docs/protocol/v2/draft/authentication.mdx

@@ -206,8 +206,7 @@ For a `terminal` method, the Client:
 3. Presents the terminal to the user and waits for the process to exit. Exit
    status zero signals success; a non-zero status, termination without an exit
    status, or cancellation signals failure.
-4. Reconnects and reinitializes the ACP Agent, then retries an operation rejected
-   for requiring authentication. For an already-inserted prompt, see
+4. On success, retries an operation rejected for requiring authentication. The Client **SHOULD** first close the existing ACP connection, start and initialize a new one, and resume with `session/resume` any sessions it wants to keep, since the running Agent may not pick up the new credentials. It **MAY** instead retry on the existing connection first, and reconnect only if the retry still fails with `auth_required`. For an already-inserted prompt, see
    [Authentication failures during session work](#authentication-failures-during-session-work).
 
 The descriptor cannot provide a command. The Client derives the command from its