Does transferring HTTP payload in multiple chunks to s3 count as multiple requests in term of pricing ?

This doc suggests you are billed for all storage, bandwidth, and requests for this multipart upload and its associated parts: https://docs.aws.amazon.com/AmazonS3/latest/userguide/mpuoverview.html#mpuploadpricing.

So for your example, assuming S3 Standard Storage Tier: 10,000 POST Object requests would cost $0.05 (10000 * $0.005 / 1000) (Pricing from here). For S3, you don't pay per GB for data-in, so the requests and storage would be your only S3 charges for the upload.

Just shooting in the dark here, but you may be able to use another S3 authorization mechanism (like presigned URLs) to avoid having to compute a SigV4 signature (which is driving you to load chunks into RAM). This may allow you to stream the entire payload from disk in a single HTTP request.