refactor: propagate context.Context through call chains

Thread context.Context from callers instead of creating
context.Background() at every call site. Engine stores its
lifecycle ctx for use by triggerAlert goroutines. TUI Model
carries ctx for store operations in Cmd closures. CLI commands
create a root ctx and thread it through openStore, seed
functions, and init methods.

Only two intentional context.Background() remain in non-root
positions: engine constructor default (overridden by Start)
and drainWrites (parent already cancelled at shutdown).

internal/monitor/monitor.go

@@ -64,6 +64,7 @@ type Engine struct {
 	dbWrites  chan dbWrite
 	writerWG  sync.WaitGroup
 	checkerWG sync.WaitGroup
+	ctx       context.Context
 	cancel    context.CancelFunc
 	stopOnce  sync.Once
 }
@@ -90,6 +91,7 @@ func newEngine(s store.Store, allowPrivateTargets bool) *Engine {
 		allowPrivateTargets: allowPrivateTargets,
 		maintRetention:      defaultMaintRetention,
 		dbWrites:            make(chan dbWrite, dbWriteBuffer),
+		ctx:                 context.Background(),
 		db:                  s,
 		strictClient: &http.Client{
 			Transport: &http.Transport{
@@ -200,6 +202,8 @@ func (e *Engine) dbWriter(ctx context.Context) {
 }
 
 // drainWrites flushes everything still buffered, best-effort, at shutdown.
+// Uses context.Background because the engine ctx is already cancelled when
+// this runs — writes still need to reach the DB.
 func (e *Engine) drainWrites() {
 	for {
 		select {
@@ -238,8 +242,8 @@ func (e *Engine) Stop() {
 	})
 }
 
-func (e *Engine) InitLogs() {
-	entries, err := e.db.LoadLogs(context.Background(), maxLogEntries)
+func (e *Engine) InitLogs(ctx context.Context) {
+	entries, err := e.db.LoadLogs(ctx, maxLogEntries)
 	if err != nil {
 		return
 	}
@@ -264,6 +268,7 @@ func (e *Engine) Start(ctx context.Context) {
 	// trace the cross-method call, and cancelling the parent reaps this child
 	// regardless, so the leak it warns about can't occur.
 	ctx, e.cancel = context.WithCancel(ctx) //nolint:gosec // cancel is called in Stop()
+	e.ctx = ctx
 
 	e.writerWG.Add(1)
 	go e.dbWriter(ctx)