feat(elixir): Add propagator, LiveView tracing, and Plug.Telemetry note (#17336)

## DESCRIBE YOUR PR

Document Sentry.OpenTelemetry.Propagator for distributed tracing via
sentry-trace and baggage headers. Add LiveView trace propagation setup
using LiveViewPropagator and Plug.LiveViewContext. Include note about
OpentelemetryPhoenix requiring Plug.Telemetry in the endpoint.

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## PRE-MERGE CHECKLIST

*Make sure you've checked the following before merging your changes:*

- [ ] Checked Vercel preview for correctness, including links
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Co-authored-by: Claude <noreply@anthropic.com>

Author: sl0thentr0py

docs/platforms/elixir/tracing/index.mdx

@@ -60,18 +60,42 @@ Set up OpenTelemetry to send traces to Sentry:
 config :opentelemetry, span_processor: {Sentry.OpenTelemetry.SpanProcessor, []}
 
 config :opentelemetry, sampler: {Sentry.OpenTelemetry.Sampler, []}
+
+# Enable distributed tracing across services via sentry-trace and baggage headers
+config :opentelemetry,
+  text_map_propagators: [
+    :trace_context,
+    :baggage,
+    Sentry.OpenTelemetry.Propagator
+  ]
 ```
 
 ## Set Up Phoenix Instrumentation
 
-In your `application.ex`, set up the OpenTelemetry instrumentation:
+In your `application.ex`, set up the OpenTelemetry instrumentation.
+
+
+<Alert title="Note">
+
+`OpentelemetryPhoenix` requires your Phoenix endpoint to include `Plug.Telemetry` in order to correctly trace endpoint calls. Make sure your endpoint contains:
+
+```elixir
+plug Plug.Telemetry, event_prefix: [:phoenix, :endpoint]
+```
+
+This is included by default in the Phoenix endpoint template.
+
+</Alert>
 
 ```elixir
 # lib/my_app/application.ex
 defmodule MyApp.Application do
   use Application
 
   def start(_type, _args) do
+    # Set up LiveView trace propagation (must be BEFORE OpentelemetryPhoenix)
+    Sentry.OpenTelemetry.LiveViewPropagator.setup()
+
     # Set up OpenTelemetry instrumentation
     OpentelemetryBandit.setup()           # for Bandit (Phoenix 1.7+)
     # OR OpentelemetryPhoenix.setup(adapter: :cowboy2)  # for Cowboy
@@ -92,6 +116,20 @@ defmodule MyApp.Application do
 end
 ```
 
+Then add `Sentry.Plug.LiveViewContext` to your router's browser pipeline, after `:fetch_session`. This stores the trace context in the session so that LiveView processes can restore it during `mount`, `handle_params`, and `handle_event` callbacks.
+
+```elixir {filename:lib/my_app_web/router.ex}
+pipeline :browser do
+  plug :accepts, ["html"]
+  plug :fetch_session
+  plug :fetch_live_flash
+  plug :put_root_layout, html: {MyAppWeb.Layouts, :root}
+  plug :protect_from_forgery
+  plug :put_secure_browser_headers
+  plug Sentry.Plug.LiveViewContext
+end
+```
+
 ## Advanced Sampling
 
 For more control over sampling, you can use a sampling function: