Unable to query SQL server metadata through linked server
The issue is not security related :-).

In your query, you are selecting from a table on a remote system, but the WHERE condition is using the OBJECT_ID() function, which can only see the local instance, and is not running in the scope of the Linked Server connection.

Why don't you try:

select *
from [DBTEST].[AdventureWorks].sys.objects
where [name] = N'DatabaseLog';


And that query makes more sense anyway since you already had the name, so no sense in querying to get the ID from the name just to use the ID in a second query ;-).

If you want / need to also filter on the Schema name, then you will have to add the JOIN to the [DBTEST].[AdventureWorks].sys.schemas table as OBJECT_SCHEMA_NAME is also local scope only.