build(client): generate eslint 9 configs for all packages (#25989)

This change updates the shared eslint 9 config to be TypeScript and
updates the script in scripts/generate-flat-eslint-configs.ts to support
a `--typescript` flag to output typescript per-package configs instead
of ESM. Also adds a `--finalize` flag that will do some additional
cleanup once packages are fully migrated to eslint 9.

Finally, there are lots of fixes to the script to handle ignore entries,
inheritance from other configs, etc. The script now produces configs
that work in my testing without any modifications. Even if that doesn't
hold true once we are truly migrating (see #25932), merging this
beforehand will simplify the review of those changes.

All the configs were generated by the script using this command:

```
tsx scripts/generate-flat-eslint-configs.ts --typescript
```

Author: tylerbutler

azure/packages/azure-local-service/eslint.config.mts

@@ -0,0 +1,22 @@
+/* eslint-disable */
+/**
+ * GENERATED FILE - DO NOT EDIT DIRECTLY.
+ * To regenerate: pnpm tsx scripts/generate-flat-eslint-configs.ts --typescript
+ */
+import type { Linter } from "eslint";
+import { strict } from "../../../common/build/eslint-config-fluid/flat.mts";
+
+const config: Linter.Config[] = [
+	...strict,
+	{
+		files: ["**/*.ts", "**/*.tsx", "**/*.mts", "**/*.cts"],
+		languageOptions: {
+			parserOptions: {
+				projectService: false,
+				project: ["./tsconfig.eslint.json"],
+			},
+		},
+	},
+];
+
+export default config;

azure/packages/azure-service-utils/eslint.config.mts

@@ -0,0 +1,33 @@
+/* eslint-disable */
+/**
+ * GENERATED FILE - DO NOT EDIT DIRECTLY.
+ * To regenerate: pnpm tsx scripts/generate-flat-eslint-configs.ts --typescript
+ */
+import type { Linter } from "eslint";
+import { strict } from "../../../common/build/eslint-config-fluid/flat.mts";
+
+const config: Linter.Config[] = [
+	...strict,
+	{
+		rules: {
+			"import-x/no-unassigned-import": "off",
+			"@typescript-eslint/strict-boolean-expressions": "off",
+			"unicorn/prevent-abbreviations": [
+				"error",
+				{
+					"allowList": {
+						"i": true,
+					},
+				},
+			],
+		},
+	},
+	{
+		files: ["src/test/types/*"],
+		rules: {
+			"unicorn/prevent-abbreviations": "off",
+		},
+	},
+];
+
+export default config;