Generalize message conversion for HTTP message content in AssertJ support

[snicoll]

Our AssertJ support has dedicated support for converting JSON to data types. Some recent work required to adapt things a bit, see #33131.

While working on this, I've come to realize that providing the raw converter isn't great as:

1. Only one converter can be used and we miss cases where specific converters could handle specific data types
2. Supporting other formats (such as XML) would require a signature change.

This issue is about trying to adapt things to address both of these issue. This should effectively supersede #33131 as we'd be handling more than one converter anyway.