feat(pageserver): integrate PostHog with gc-compaction rollout (#11917)

## Problem

part of https://github.com/neondatabase/neon/issues/11813

## Summary of changes

* Integrate feature store with tenant structure.
* gc-compaction picks up the current strategy from the feature store.
* We only log them for now for testing purpose. They will not be used
until we have more patches to support different strategies defined in
PostHog.
* We don't support property-based evaulation for now; it will be
implemented later.
* Evaluating result of the feature flag is not cached -- it's not
efficient and cannot be used on hot path right now.
* We don't report the evaluation result back to PostHog right now.

I plan to enable it in staging once we get the patch merged.

---------

Signed-off-by: Alex Chi Z <chi@neon.tech>

libs/pageserver_api/src/config.rs

@@ -45,6 +45,21 @@ pub struct NodeMetadata {
     pub other: HashMap<String, serde_json::Value>,
 }
 
+/// PostHog integration config.
+#[derive(Debug, Clone, PartialEq, Eq, serde::Serialize, serde::Deserialize)]
+pub struct PostHogConfig {
+    /// PostHog project ID
+    pub project_id: String,
+    /// Server-side (private) API key
+    pub server_api_key: String,
+    /// Client-side (public) API key
+    pub client_api_key: String,
+    /// Private API URL
+    pub private_api_url: String,
+    /// Public API URL
+    pub public_api_url: String,
+}
+
 /// `pageserver.toml`
 ///
 /// We use serde derive with `#[serde(default)]` to generate a deserializer
@@ -186,6 +201,8 @@ pub struct ConfigToml {
     pub tracing: Option<Tracing>,
     pub enable_tls_page_service_api: bool,
     pub dev_mode: bool,
+    #[serde(skip_serializing_if = "Option::is_none")]
+    pub posthog_config: Option<PostHogConfig>,
     pub timeline_import_config: TimelineImportConfig,
     #[serde(skip_serializing_if = "Option::is_none")]
     pub basebackup_cache_config: Option<BasebackupCacheConfig>,
@@ -701,6 +718,7 @@ impl Default for ConfigToml {
                 import_job_checkpoint_threshold: NonZeroUsize::new(128).unwrap(),
             },
             basebackup_cache_config: None,
+            posthog_config: None,
         }
     }
 }