ci: upload server and client coverage reports to codecov (#183)

* ci: upload server and client coverage reports to codecov

Generate client lcov output and publish per-package coverage from CI so Codecov checks and README coverage artifacts stay up to date.

* ci: configure codecov project status and pr comments

* ci: isolate codecov coverage status by flags

* ci: add patch coverage status, per-flag badges, and client coverage scope

- Add patch coverage status in codecov.yml (server and client flags) so
  Codecov checks coverage on changed lines in PRs, not just overall trend
- Add include/exclude patterns to client vitest coverage config so test
  files and entry points are excluded from coverage stats
- Add per-flag server/client coverage badges to the README coverage section

* docs: restructure coverage map in README

Move the coverage map down to the documentation and contributing section, giving it its own heading. Remove the redundant server and client badges from the top.

codecov.yml

@@ -0,0 +1,61 @@
+coverage:
+  status:
+    project:
+      default:
+        target: auto
+        threshold: 0%
+        base: auto
+        flags:
+          - server
+          - client
+      server:
+        target: auto
+        threshold: 0%
+        base: auto
+        flags:
+          - server
+      client:
+        target: auto
+        threshold: 0%
+        base: auto
+        flags:
+          - client
+    patch:
+      default:
+        target: auto
+        threshold: 0%
+        base: auto
+        flags:
+          - server
+          - client
+      server:
+        target: auto
+        threshold: 0%
+        base: auto
+        flags:
+          - server
+      client:
+        target: auto
+        threshold: 0%
+        base: auto
+        flags:
+          - client
+
+comment:
+  layout: "diff, flags, files"
+  behavior: default
+  require_changes: false
+  require_base: false
+  require_head: true
+  hide_project_coverage: false
+  show_carryforward_flags: true
+
+flags:
+  server:
+    paths:
+      - server/**
+    carryforward: true
+  client:
+    paths:
+      - client/**
+    carryforward: true