feat(ai): compat entrypoint, core-only root barrel (phase 5)

The root barrel is now core-only and side-effect free: types,
createModels/createProvider, auth substrate, lazyStream/lazyApi, faux,
utils. Generated catalogs, api-registry, env-api-keys, images, global
stream functions, and per-API lazy wrappers leave the root.

New @earendil-works/pi-ai/compat preserves the old surface verbatim as
a strict superset of the root: api-dispatch stream/complete with env
key injection, the builtin registration side effect (skip-if-present so
it cannot clobber earlier overrides), deprecated getModel/getModels/
getProviders aliases of the new getBuiltin* reads in providers/all,
lazy api wrappers + setBedrockProviderModule, and image generation.
Compat dies with the coding-agent ModelManager migration.

Packaging: exports map gains ./compat, ./providers/*, ./api/*;
sideEffects array lists only the effectful modules.

Old-global imports across agent/coding-agent/examples and pi-ai tests
switch to /compat (path-only; compat is a superset). The coding-agent
extension loader resolves the pi-ai ROOT specifier to compat, so
existing user extensions using the old global API keep working at
runtime until compat is removed. vitest configs alias /compat to src;
browser smoke imports old globals from /compat.

packages/coding-agent/examples/extensions/custom-compaction.ts

@@ -13,7 +13,7 @@
  *   pi --extension examples/extensions/custom-compaction.ts
  */
 
-import { complete } from "@earendil-works/pi-ai";
+import { complete } from "@earendil-works/pi-ai/compat";
 import type { ExtensionAPI } from "@earendil-works/pi-coding-agent";
 import { convertToLlm, serializeConversation } from "@earendil-works/pi-coding-agent";
 

packages/coding-agent/examples/extensions/custom-provider-gitlab-duo/index.ts

@@ -21,7 +21,7 @@ import {
 	openAIResponsesApi,
 	type SimpleStreamOptions,
 	type ThinkingLevelMap,
-} from "@earendil-works/pi-ai";
+} from "@earendil-works/pi-ai/compat";
 import type { ExtensionAPI } from "@earendil-works/pi-coding-agent";
 
 // =============================================================================

packages/coding-agent/examples/extensions/custom-provider-gitlab-duo/test.ts

@@ -8,7 +8,7 @@
  *   npx tsx test.ts claude-sonnet-4-5-20250929 --thinking
  */
 
-import { type Api, type Context, type Model, registerApiProvider, streamSimple } from "@earendil-works/pi-ai";
+import { type Api, type Context, type Model, registerApiProvider, streamSimple } from "@earendil-works/pi-ai/compat";
 import { readFileSync } from "fs";
 import { getAgentDir } from "packages/coding-agent/src/config.js";
 import { join } from "path";

packages/coding-agent/examples/extensions/handoff.ts

@@ -13,7 +13,7 @@
  */
 
 import type { AgentMessage } from "@earendil-works/pi-agent-core";
-import { complete, type Message } from "@earendil-works/pi-ai";
+import { complete, type Message } from "@earendil-works/pi-ai/compat";
 import type { ExtensionAPI, SessionEntry } from "@earendil-works/pi-coding-agent";
 import { BorderedLoader, convertToLlm, serializeConversation } from "@earendil-works/pi-coding-agent";
 

packages/coding-agent/examples/extensions/qna.ts

@@ -7,7 +7,7 @@
  * 3. Loads the result into the editor for user to fill in answers
  */
 
-import { complete, type UserMessage } from "@earendil-works/pi-ai";
+import { complete, type UserMessage } from "@earendil-works/pi-ai/compat";
 import type { ExtensionAPI } from "@earendil-works/pi-coding-agent";
 import { BorderedLoader } from "@earendil-works/pi-coding-agent";
 

packages/coding-agent/examples/extensions/summarize.ts

@@ -1,4 +1,4 @@
-import { complete, getModel } from "@earendil-works/pi-ai";
+import { complete, getModel } from "@earendil-works/pi-ai/compat";
 import type { ExtensionAPI, ExtensionCommandContext } from "@earendil-works/pi-coding-agent";
 import { DynamicBorder, getMarkdownTheme } from "@earendil-works/pi-coding-agent";
 import { Container, Markdown, matchesKey, Text } from "@earendil-works/pi-tui";