fix(copilot): propagate parent context instead of using context.Background() in internal functions

[jongio]

Summary

Several functions create fresh context.Background() contexts internally instead of accepting a parent context parameter, preventing callers from propagating cancellation or deadlines.

Current Pattern

internal/update/check.go (line 170):

func fetchLatestVersion() (string, error) {
    client := newSecureClient(apiTimeout)
    req, err := http.NewRequestWithContext(context.Background(), http.MethodGet, latestReleaseURL, nil)
    // ...
}

internal/update/update.go (lines 188, 225):

req, err := http.NewRequestWithContext(context.Background(), http.MethodGet, url, nil)
// ...
req, err := http.NewRequestWithContext(context.Background(), http.MethodGet, checksumURL, nil)

internal/tui/components/reindex.go (line 41):

ctx, cancel := context.WithCancel(context.Background())

internal/copilot/client.go (lines 300, 363, 422, 499, 555, 609):
Multiple operations create context.WithTimeout(context.Background(), ...) instead of deriving from a caller-supplied context.

Idiomatic Replacement

Accept ctx context.Context as the first parameter per Go convention, and derive child contexts from it:

func fetchLatestVersion(ctx context.Context) (string, error) {
    client := newSecureClient(apiTimeout)
    req, err := http.NewRequestWithContext(ctx, http.MethodGet, latestReleaseURL, nil)
    // ...
}

For cases where a timeout is needed, derive from the parent:

initCtx, initCancel := context.WithTimeout(ctx, searchOperationTimeout)

Why It Matters

• Using context.Background() in internal functions breaks the cancellation chain — if the application is shutting down, these HTTP requests and operations continue running until their own timeout expires
• Go convention: "Incoming requests to a server should create a Context, and outgoing calls to servers should accept a Context" (Go blog)
• The update check and download functions do network I/O that should be cancellable by the caller
• This also prevents proper tracing/observability since context values are lost

Files Affected

File	Lines	Issue
internal/update/check.go	170	fetchLatestVersion uses context.Background()
internal/update/update.go	188, 225	download and checksum fetch use context.Background()
internal/copilot/client.go	300, 363, 422, 499, 555, 609	SDK init and search create root contexts
internal/tui/components/reindex.go	41	Reindex creates root context

[jongio]

Consolidated into a single tracking issue.