Is data transfer billed for synchronous Lambda-to-Lambda Invoke within the same region?

I'm building a tool that reads a serverless application's call graph and recommends which Lambda functions could be merged into a single deployment. Part of the cost model prices the data that flows between functions, on the basis that merging two functions turns a network call into an in-process one.

I need to know whether that data is actually billed. When function A invokes function B through the Lambda API in the same region (ap-south-1 in my case), is the request or response payload charged as data transfer?

The Lambda pricing page says in-region data transfer is free between Lambda and S3, DynamoDB, SQS, SNS, Kinesis, EFS and several others. Lambda-to-Lambda is not on that list, so I can't tell whether it's an omission or deliberate. The page also says data transferred in and out "from outside the region the function executed" is charged at EC2 rates, which implies same-region is treated differently, but doesn't say what happens for Lambda talking to Lambda.

I checked my own bill and everything reads $0.00, but my usage sits inside the free tier so that can't distinguish "not billed" from "billed and absorbed".

my model currently charges $0.01/GiB on every call that crosses a function boundary, and that term accounts for essentially the entire cost saving the tool reports. If in-region invoke payloads aren't billed, that saving isn't real and I need to rebuild the model around latency and cold start reduction instead. I'd rather find that out from someone who knows than from a user's bill.