Fix Programs quick-filter empty states

[quntao-z]

Summary

• Make the Programs & Fellowships result counter reflect the active quick filter.
• Add useful Open Only and Closing Soon zero-result states that point students to Next Cycle when available.
• Keep local quick-filter pagination moving until server results are exhausted, so later pages can still supply matches.

Validation

• yarn --cwd client test:ci src/pages/tests/fellowships.test.tsx src/hooks/tests/useInfiniteScroll.test.tsx
• yarn --cwd client test:ci
• yarn --cwd client build
• yarn build
• graphify update .
• no-mistakes: review, test, document, lint, push, and PR gates completed on the corrected commit path; rebase was skipped because this yLabs work targets beta and the tool rebases to main/default. The CI gate could not complete because GitHub reported no CI checks configured for the generated PR.