fix(eid-wallet): settle the settings store before the app is killed

[Sahil2004]

Description of change

Closing the app from the background intermittently signed the user out, dropping them back to the create-or-restore splash with their vault, user, PIN and document gone.

The settings store is saved by tauri-plugin-store with fs::write, which opens the file with O_TRUNC, so the previous contents are discarded before the new bytes are written. Auto-save is debounced and Android kills backgrounded apps with SIGKILL, so a save is frequently still in flight when the kill lands. Interrupting that write leaves global-state.json at zero bytes, and the next launch reads an empty store, concludes this is a first run and persists a fresh onboarding state over the top, which makes the loss permanent.

An app is only killed after it has been backgrounded, and the webview still receives visibilitychange at that point. Use it as the settling point: flush the store so no debounced write remains outstanding, then copy the settled file into a sidecar backup written atomically via a temp file, fsync and rename. Once that completes there is no write left for a kill to interrupt.

Loading falls back to the sidecar when the primary file cannot be parsed, which covers a kill that arrives before the flush finishes; the backup then still holds the previous complete state. Recovery keys off unparseable bytes rather than an absent or empty cache, so a session the user ended deliberately is never resurrected: clearing the store on logout serialises to "{}", which is valid JSON and is passed through untouched. Backing up refuses to copy a primary that does not parse, so a damaged file cannot overwrite a good backup. With no readable backup the original parse error is returned and a genuine first launch still runs normal setup instead of receiving invented state.

All of this runs at backgrounding only. The startup and steady-state save paths are untouched, so launch performs no extra filesystem work.

Issue Number

Closes #1143

Type of change

• Fix (a change which fixes an issue)

How the change has been tested

Manually.

Change checklist

• I have ensured that the CI Checks pass locally
• I have removed any unnecessary logic
• My code is well documented
• I have signed my commits
• My code follows the pattern of the application
• I have self reviewed my code

[coderabbitai]

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[Bekiboo]

Audit pass. None of these are blocking.