Install scripts do not auto-set Daemon.UpdateChannel when using --channel beta

Problem

When users opt into the beta release channel via --channel beta, the install script downloads the correct beta binary but does not persist Daemon.UpdateChannel: "beta" into netclaw.json. This causes the daemon's self-update mechanism to default to stable channel (the default) and compare against the latest stable release instead of the latest prerelease.

Symptoms

• User runs curl ... | bash -s -- --channel beta (or the equivalent on Windows/Docker)
• The correct beta binary is installed
• netclaw update --check reports up to date even when a newer beta is available
• The daemon's background update check also reports no updates

Root Cause

The install scripts (install.sh, install.ps1) accept --channel beta and use it to resolve the version from the manifest's latestPrerelease pointer, but they never write Daemon.UpdateChannel: "beta" to the config file.

Meanwhile, DaemonConfig defaults UpdateChannel to UpdateChannel.Stable when the config key is missing:

// DaemonConfig.cs line 54
public UpdateChannel UpdateChannel { get; init; } = UpdateChannel.Stable;

And the update checker only uses LatestPrerelease when the channel is explicitly beta:

// UpdateCheckService.cs line 258
var targetVersion = channel == UpdateChannel.Beta && !string.IsNullOrEmpty(manifest.LatestPrerelease)
    ? manifest.LatestPrerelease
    : manifest.Latest;

Steps to Reproduce

1. Install a beta version via install script with --channel beta
2. Run netclaw update --check
3. Observe: reports up to date even when a newer beta is available
4. Fix (manual): jq '.Daemon.UpdateChannel = "beta"' ~/.netclaw/config/netclaw.json

Proposed Fix

Both install.sh and install.ps1 should auto-write Daemon.UpdateChannel: "beta" into the config when --channel beta is passed and an existing config file is present.

For install.sh, a jq-based patch would look like:

if [ "$CHANNEL" = "beta" ] && [ "$DRY_RUN" = false ]; then
    CONFIG_FILE="$HOME/.netclaw/config/netclaw.json"
    if [ -f "$CONFIG_FILE" ] && command -v jq >/dev/null 2>&1; then
        jq '.Daemon.UpdateChannel = "beta"' "$CONFIG_FILE" > "${CONFIG_FILE}.tmp" && \
            mv "${CONFIG_FILE}.tmp" "$CONFIG_FILE"
        echo "  Updated UpdateChannel to 'beta' in $CONFIG_FILE"
    fi
fi

The Windows installer should do the equivalent with PowerShell's ConvertFrom-Json / ConvertTo-Json, and Docker instructions should explicitly call out this config requirement.

Affected Files

• scripts/install.sh
• scripts/install.ps1
• docs/getting-started/installation.md (ensure config requirement is prominent)