The way you would have to go about it is enabling PopulateQueryMetrics in the SDK.
Ones enabled your queries will have the x-ms-documentdb-query-metrics header populated. The value looks like this:
totalExecutionTimeInMs=33.67;queryCompileTimeInMs=0.06;queryLogicalPlanBuildTimeInMs=0.02;queryPhysicalPlanBuildTimeInMs=0.10;queryOptimizationTimeInMs=0.00;VMExecutionTimeInMs=32.56;indexLookupTimeInMs=0.36;documentLoadTimeInMs=9.58;systemFunctionExecuteTimeInMs=0.00;userFunctionExecuteTimeInMs=0.00;retrievedDocumentCount=2000;retrievedDocumentSize=1125600;outputDocumentCount=2000;writeOutputTimeInMs=18.10;indexUtilizationRatio=1.00
As you can see this needs be to split and parsed but it has a lot of useful info which you can log and query to see a lot of stuff about your queries and their performance.
You can read more about query metrics here: https://learn.microsoft.com/en-us/azure/cosmos-db/sql-api-query-metrics