It is not possible to get the size of specific indexes. You can however see the size of all indexes via portal or diagnostic logs. You can also set alerts on storage size as well.
To see index size in portal to your Cosmos account in Azure Portal then Metrics, select Storage tab, then select your database and collection.
For more information on setting alerts see, https://video2.skills-academy.com/en-us/azure/cosmos-db/create-alerts
For more information on querying diagnostic logs for storage metrics see, https://video2.skills-academy.com/en-us/azure/cosmos-db/monitor-cosmos-db-reference