jsoncpp: modernize Reader/Writer to the 1.x builder API (post-vcpkg-migration)

Follow-up to the jsoncpp vcpkg migration (#179). The migration is done in two steps:

• Step 1 (vcpkg move): migrate //thirdparty/jsoncpp to vcpkg jsoncpp 1.9.x, keeping flare's existing Json::Reader/FastWriter/StyledWriter usage and silencing their deprecation with -Wno-deprecated-declarations on the consuming targets. This isolates the library/version change from any API rewrite.
• Step 2 (this issue): replace the deprecated APIs with the 1.x builder API so we can drop the warning suppression (and stay compatible past jsoncpp's eventual removal of the legacy classes).

Scope

Deprecated APIs are used in ~23 files / ~12 targets (http builtin handlers, binlog, base/option, monitoring, plus tests):

• Json::Reader (≈21 sites) → Json::CharReaderBuilder + Json::parseFromStream / CharReader::parse.
• Json::FastWriter (≈4) / Json::StyledWriter (≈8) → Json::StreamWriterBuilder + Json::writeString.

Behavioral pitfalls to handle in the rewrite

• FastWriter::write() appends a trailing \n; writeString() does not. StreamWriterBuilder defaults to pretty output — set builder["indentation"]="" for compact. Update golden/string-compare tests accordingly.
• 1.x throws Json::LogicError/RuntimeError on type misuse (e.g. asString() on a non-string) where 0.x coerced/defaulted.
• 1.x parsing is stricter; revisit any inputs relying on 0.x leniency.

Optional cleanup

• Switch includes from flare's jsoncpp/<h> alias to the canonical json/<h> and drop the include_prefix={'jsoncpp':'json'} mapping added in Step 1.

🤖 Generated with Claude Code

Locate the deprecated Json::Reader, FastWriter, and StyledWriter uses across the http builtin handlers, binlog, base/option, monitoring, and tests. Start by tracing each use and its existing string or golden-test expectations. Replace the APIs with the 1.x builders, preserve compact output and trailing-newline behavior, update affected comparisons, and verify the warning suppression can be removed.