Bug: Deleted no-code experiments still being returned via API

[luke-belton]

Bug Description

Web experiment API endpoints (https://posthog.com/docs/api/web-experiments) are still returning deleted no-code experiments.

Semi related to https://github.com/PostHog/posthog/issues/33069

Additional context

https://posthoghelp.zendesk.com/agent/tickets/32381

Debug info

- [ ] PostHog Cloud, Debug information: [please copy/paste from https://us.posthog.com/settings/project-details#variables or https://eu.posthog.com/settings/project-details#variables]
- [ ] PostHog Hobby self-hosted with `docker compose`, version/commit: [please provide]
- [ ] PostHog self-hosted with Kubernetes (deprecated, see [`Sunsetting Kubernetes support`](https://posthog.com/blog/sunsetting-helm-support-posthog)), version/commit: [please provide]