fix(den): harden billing display and UI

[shizhigu]

Why

Checkout and billing are money-related surfaces. The displayed price, cadence, and entitlement copy should come from the billing display path, and local screenshot mocks should not render on app.openworklabs.com.

What changed

• Reused shared billing helpers for checkout and billing dashboard price/status copy.
• Adjusted Den checkout and billing layout to match the OpenWork shell without changing backend behavior.
• Added a host-aware mock guard so NEXT_PUBLIC_DEN_MOCK_BILLING is ignored on app.openworklabs.com.
• Wired billing helper tests into CI.

Test plan

• pnpm --filter @openwork-ee/den-web test:billing
• pnpm --filter @openwork-ee/den-web exec tsc --noEmit
• pnpm --filter @openwork-ee/den-web build
• git diff --check
• rg "\\$50|50/month|50/mo" ee/apps/den-web/app ee/apps/den-web/components found no matches

Evidence

Surface	Before	After
Checkout desktop
Checkout mobile
Billing dashboard

Notes

• Den API / Polar backend behavior is unchanged.
• Pricing model is unchanged.
• Vercel fork previews require team authorization, so evidence is from local runs.

[vercel]

The latest updates on your projects. Learn more about Vercel for GitHub.

Project	Deployment	Actions	Updated (UTC)
openwork-landing	Ready	Preview, Comment, Open in v0	May 1, 2026 5:19pm

[vercel]

@shizhigu is attempting to deploy a commit to the Different AI Team on Vercel.

A member of the Team first needs to authorize it.

[github-actions]

The following comment was made by an LLM, it may be inaccurate:

[src-opn]

we will be replacing all billing items with a dedicated billing module soon.
WIll leave this pr open for now and see if we can rebase changes to new module once released