Movin.ie Web-Based Mobile App Development

About: Movin.ie is a live Irish residential property marketplace (sales, rentals, room shares, summer lets). The website is already built and live, with a responsive mobile design (vanilla JS frontend, Node.js/Express backend, PostgreSQL database, already deployed).

What we need: We want to turn our existing responsive website into a mobile app for iOS and Android using a web-based / wrapper approach (e.g. Capacitor, or a PWA). We do NOT want a fully native app rebuilt from scratch. The app should use our existing website and backend — not rebuild them.

Scope:

Package our existing responsive website as a mobile app for the App Store and Google Play (Capacitor or similar), OR set it up as an installable PWA — please advise which you'd recommend and why
Ensure it looks and works well as an app (proper app icon, splash screen, smooth navigation, no broken mobile behaviour)
Add push notifications (e.g. for new listings / saved-search alerts) if feasible within the web-based approach
Handle App Store and Google Play submission and setup

What we'll provide: The live website, access to our backend, brand assets (logo, colours, fonts), and any developer accounts needed.

Please include in your proposal:

Your recommended web-based approach (Capacitor wrapper vs PWA) and why
Fixed-price quote
Timeline
What's included for App Store / Google Play submission
Ongoing maintenance/support terms (and what updates cost after launch)

Note: We're specifically looking for a cost-effective web-based solution, not a native rebuild. Please only quote on that basis.