The Cost and Usage Report (CUR) from AWS is just a fine-grained listing of all the resources in your account and their cost. It can be dumped out on different schedules (hourly, daily, monthly) and in different formats (CSV, Parquet).
It is pretty common to configure the CUR files to be dumped into your S3 account and query them via Athena. Athena is billed as $ per TB scanned ($5 last time I looked), so the cost will be based on how often the data is being queried. Downside is that each query can take quite a while to execute depending on data size.
The other common option is to ingest the CUR data into Redshift which gives you better control / options for performance, manipulation, etc. but requires that you set up and manage Redshift.
Hard to tell exactly what the Athena cost here would be as it depends on the number of assets in the account and the frequency in which you are querying the CUR. However, you can issue quite a bit of Athena queries on CUR data for most AWS use cases without incurring too much cost. Unless you have a rapidly changing environment (e.g. hundreds of k of assets turning over daily) or just tons of standing assets, you should be safe to assume hundreds a day at the most? Probably much less for most use cases. This is assuming they are querying once and storing rather than real time querying all the time and normal usage patters, etc.
Does the Athena does the actual processing/computation of costs ? What is the usual cost for running Athena ?
It also seems strange that I have to put the IAM keys into secrets instead of using IAM role for service account for configuring it.