[source-productboard] v1 API retired by Productboard, migrate to v2

### Connector Name

source-productboard

### Connector Version

0.0.63

### What step the error happened?

Configuring a new connector

### Relevant information

Productboard has **retired the v1 REST API**. `source-productboard` calls v1
endpoints with the `X-Version: "1"` header, so **every sync on this connector
now fails**

[productboard_error_logs.txt](https://github.com/user-attachments/files/30351593/productboard_error_logs.txt)

this affects all users of the connector, not a single workspace.

Migration guide: https://developer.productboard.com/reference/migration-guide

### Relevant log output

```shell
2026-07-24 12:01:06 source ERROR Max retry limit reached after 10.5s. Request: , Response:
2026-07-24 12:01:06 source ERROR Retries exhausted with backoff exception.
Traceback (most recent call last):
File "/usr/local/lib/python3.13/site-packages/airbyte_cdk/sources/streams/http/http_client.py", line 292, in _send_with_retry
response = backoff_handler(rate_limit_backoff_handler(user_backoff_handler))(
request,
...<2 lines>...
exit_on_rate_limit=exit_on_rate_limit,
) # type: ignore # mypy can't infer that backoff_handler wraps _send
File "/usr/local/lib/python3.13/site-packages/backoff/_sync.py", line 105, in retry
ret = target(*args, **kwargs)
File "/usr/local/lib/python3.13/site-packages/backoff/_sync.py", line 105, in retry
ret = target(*args, **kwargs)
File "/usr/local/lib/python3.13/site-packages/backoff/_sync.py", line 105, in retry
ret = target(*args, **kwargs)
File "/usr/local/lib/python3.13/site-packages/airbyte_cdk/sources/streams/http/http_client.py", line 386, in _send
self._handle_error_resolution(
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~^
response=response,
^^^^^^^^^^^^^^^^^^
...<3 lines>...
exit_on_rate_limit=exit_on_rate_limit,
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
)
^
File "/usr/local/lib/python3.13/site-packages/airbyte_cdk/sources/streams/http/http_client.py", line 541, in _handle_error_resolution
raise UserDefinedBackoffException(
...<5 lines>...
)
airbyte_cdk.sources.streams.http.exceptions.UserDefinedBackoffException: Response was not ok: `410 Client Error: Gone for url: https://api.productboard.com/products`. Response content is: {"message":"The Productboard API v1 has been retired for this workspace. Migrate to API v2 — see https://developer.productboard.com/reference/migration-guide"}
```

### Contribute

- [x] Yes, I want to contribute

---
**Internal Tracking:** airbytehq/oncall#13152

Start by locating the source-productboard connector implementation and identify its v1 endpoint calls and X-Version: "1" header. Read Productboard's migration guide, then update the connector for v2 and validate that configuring and syncing no longer produces the reported 410 response for the affected products endpoint.

Escrita pelo modelo de indexação a partir do texto da issue.