[android - dialog] Showing any dialog (open / save) does not resolve the underlying Promise the first time

### Describe the bug

Or in other words, if you open() the first time, nothing happens, and when you open() another time, both promises (first open, second open) will resolve.

This is annoying as hell.

### Reproduction

- open() or save() once through a button (this is how I did it)
- await the resulting promise (console.log ?)
- see that it hangs
- open() again
- see both promises resolve at the same time

### Expected behavior

Behaviour should be consistent across macOS/Linux/Windows/iOS where it works right the first time.

### Full `tauri info` output

```text
[✔] Environment
- OS: Artix Linux Rolling Release x86_64 (X64) (Unknown DE on wayland)
✔ webkit2gtk-4.1: 2.50.6
✔ rsvg2: 2.61.4
✔ rustc: 1.86.0 (05f9846f8 2025-03-31)
✔ cargo: 1.86.0 (adf9b6ad1 2025-02-28)
✔ rustup: 1.28.2 (2026-02-27)
✔ Rust toolchain: stable-x86_64-unknown-linux-gnu (overridden by environment variable RUSTUP_TOOLCHAIN)
- node: 25.8.1
- yarn: 1.22.22
- npm: 11.11.1
- deno: deno 2.7.7

[-] Packages
- tauri 🦀: 2.10.2
- tauri-build 🦀: 2.5.5
- wry 🦀: 0.54.1
- tao 🦀: 0.34.5
- tauri-cli 🦀: 2.7.0
- @tauri-apps/api : 2.10.1
- @tauri-apps/cli : 2.6.3

[-] Plugins
- tauri-plugin-biometric 🦀: 2.3.2
- @tauri-apps/plugin-biometric : 2.3.2
- tauri-plugin-opener 🦀: 2.5.3
- @tauri-apps/plugin-opener : 2.5.3
- tauri-plugin-process 🦀: 2.3.1
- @tauri-apps/plugin-process : 2.3.1
- tauri-plugin-dialog 🦀: 2.6.0
- @tauri-apps/plugin-dialog : 2.6.0
- tauri-plugin-os 🦀: 2.3.2
- @tauri-apps/plugin-os : 2.3.2
- tauri-plugin-store 🦀: 2.4.2
- @tauri-apps/plugin-store : 2.4.2
- tauri-plugin-fs 🦀: 2.4.5
- @tauri-apps/plugin-fs : 2.4.5
- tauri-plugin-http 🦀: 2.5.7
- @tauri-apps/plugin-http : 2.5.7

[-] App
- build-type: bundle
- CSP: unset
- frontendDist: ../dist
- devUrl: http://localhost:5173/
- framework: Vue.js
- bundler: Vite
```

### Stack trace

```text

```

### Additional context

_No response_