feat: add native clipboard support for screenshot paste (#67)

## Summary
- Adds Tauri clipboard-manager plugin to read images from native clipboard
- Falls back to native clipboard when WebView clipboard API returns empty (fixes screenshot paste)
- Allows sending messages with just attachments (no text required)
- Logs attached files to output with 📎 emoji

## Test plan
- [ ] Build and run the app natively on Windows
- [ ] Copy a screenshot (Win+Shift+S) and paste in the chat input
- [ ] Verify the screenshot appears as an attachment preview
- [ ] Send the attachment and verify Claude receives the file path
- [ ] Test sending a message with only an attachment (no text)
- [ ] Verify the 📎 log line shows the attached filename

**Note:** Paste will not work in WSLg dev environment due to clipboard isolation - needs native Windows build to test.

✨ This PR was created with help from Hikari~ 🌸

Co-authored-by: Hikari <hikari@nhcarrigan.com>
Reviewed-on: #67
Co-authored-by: Naomi Carrigan <commits@nhcarrigan.com>
Co-committed-by: Naomi Carrigan <commits@nhcarrigan.com>

pnpm-lock.yaml

@@ -11,6 +11,9 @@ importers:
       '@tauri-apps/api':
         specifier: ^2
         version: 2.9.1
+      '@tauri-apps/plugin-clipboard-manager':
+        specifier: ^2.3.2
+        version: 2.3.2
       '@tauri-apps/plugin-dialog':
         specifier: ^2
         version: 2.6.0
@@ -735,6 +738,9 @@ packages:
     engines: {node: '>= 10'}
     hasBin: true
 
+  '@tauri-apps/plugin-clipboard-manager@2.3.2':
+    resolution: {integrity: sha512-CUlb5Hqi2oZbcZf4VUyUH53XWPPdtpw43EUpCza5HWZJwxEoDowFzNUDt1tRUXA8Uq+XPn17Ysfptip33sG4eQ==}
+
   '@tauri-apps/plugin-dialog@2.6.0':
     resolution: {integrity: sha512-q4Uq3eY87TdcYzXACiYSPhmpBA76shgmQswGkSVio4C82Sz2W4iehe9TnKYwbq7weHiL88Yw19XZm7v28+Micg==}
 
@@ -2286,6 +2292,10 @@ snapshots:
       '@tauri-apps/cli-win32-ia32-msvc': 2.9.6
       '@tauri-apps/cli-win32-x64-msvc': 2.9.6
 
+  '@tauri-apps/plugin-clipboard-manager@2.3.2':
+    dependencies:
+      '@tauri-apps/api': 2.9.1
+
   '@tauri-apps/plugin-dialog@2.6.0':
     dependencies:
       '@tauri-apps/api': 2.9.1