## Summary of changes

Use the new `PostAsJsonAsync` API to avoid serializing to string and
byte array locally

## Reason for change

We recently added support for `PostAsJsonAsync` in
#8017, and this is a good
example where we can easily swap it in in the new Exposures API used by
FFE: #7896

## Implementation details

Just updated to use the new APIs. A couple of points to notice:

- This doesn't enable gzip. If the endpoint supports it, we should
probably enable that, but would need testing
- This changes the serialization settings, by using
`SerializationHelpers.DefaultJsonSettings`, which omits serializing null
members, and uses snake-case serialization, instead of the PascalCase we
have currently
- However, [looking at the
spec](https://github.com/DataDog/dd-source/blob/main/domains/evp-workers/apps/exposures-worker/schemas/batched_exposures.json),
I'm pretty sure we're not compliant today, and what we're changing to is
correct
  - Which suggests we're missing tests...

## Test coverage

This _should_ be covered by existing tests... and if it's not, then we
need to add those tests 😄