feat: propagate PL24 part metadata, improve auth UX with Google sign-in prominence

- Add unavailable/remark/modelCodes/presel fields to categories and parts DB schema
- Pass PL24 unavailable flag through pipeline instead of filtering out records
- Show unavailable categories/parts at reduced opacity in grid, tree, and parts panel
- Display part remark and model codes as secondary info in parts table
- Move Google sign-in button above email form on login/register pages with branded icon
- Add public email existence check endpoint for better login error messages
- Update INDEX.md documentation

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

apps/api/src/users/users.controller.ts

@@ -1,6 +1,7 @@
 import { Controller, Get, Patch, Post, Delete, Body, Param, Query, UseGuards } from "@nestjs/common";
 import { UsersService } from "./users.service";
 import { CurrentUser } from "../common/decorators/current-user.decorator";
+import { Public } from "../common/decorators/public.decorator";
 import { Roles } from "../common/decorators/roles.decorator";
 import { RolesGuard } from "../common/guards/roles.guard";
 
@@ -8,6 +9,13 @@ import { RolesGuard } from "../common/guards/roles.guard";
 export class UsersController {
   constructor(private usersService: UsersService) {}
 
+  @Public()
+  @Post("check-email")
+  async checkEmail(@Body() body: { email: string }) {
+    const user = await this.usersService.findByEmail(body.email);
+    return { exists: !!user };
+  }
+
   @Get("me")
   async getMe(@CurrentUser("id") userId: string) {
     return this.usersService.findById(userId);