[Dashboard] Resume mode should require or warn about a missing application name

### Is there an existing issue for this?

- [x] I have searched the existing issues

### Describe the bug

When `ApplicationName` is missing or whitespace, `DashboardRunStore` falls back to the fixed name `Aspire`. Unrelated standalone Dashboard sessions using `--persistence Resume` and the same data root therefore reuse the same database.

The documentation demonstrates supplying a stable application name, but the CLI neither requires one nor warns that omission selects a shared per-user identity.

### Expected Behavior

`Resume` should require a stable application name, derive a context-specific identity, or clearly warn that the default identity will reuse data across standalone sessions.

### Steps To Reproduce

1. From one working directory, run `aspire dashboard run --persistence Resume` with an isolated data root.
2. Stop the Dashboard.
3. Repeat from an unrelated working directory with the same data root.
4. Both sessions use `Aspire-6b6645454dc0e896/dashboard.db`.

### Exceptions (if any)

N/A

### Aspire doctor output

```plain
Aspire CLI 13.6.0-pr.18924.g5ee63941
Ubuntu 24.04.3
```

### Anything else?

Related to #18924. Source: `src/Aspire.Dashboard/ServiceClient/DashboardRunStore.cs:105,538-545`. The behavior remains on current `main`.

Start in src/Aspire.Dashboard/ServiceClient/DashboardRunStore.cs at lines 105 and 538-545, then trace how a missing ApplicationName is used for --persistence Resume. Reproduce the two-working-directory scenario with a shared data root. Done means omission is rejected, gets a context-specific identity, or clearly warns that the default identity reuses data.

Written by the indexing model from the issue text.