There is no timestamp for the log message in the Output window after importing a document into a collection

[v-xinda]

OS: All
Build Version: 20231007.1
Regression: Not a regression

Repro steps:

1. Make sure the setting "Azure Databases: Enable Output Timestamps" is checked.
2. Create a Mongo DB account -> Create a database -> Create a collection.
3. Right click the collection -> Click "Import Document into a Collection..." -> Select a .Json file -> Import.
4. Check whether there is a timestamp for the log message in the Output window.

Expect:
There is a timestamp for the log message in the Output window.

Actual:
There is no timestamp for the log message in the Output window.

More Info:
This issue also reproduces after creating a new function query or Stored Procedure Query for the PostgreSQL account.

[JasonYeMSFT]

This is because these messages are written using an API that doesn't respect the timestamp setting.