Answers
Is a web app slower than a native app?
For messaging, no — the difference is imperceptible. Where native still wins is background behaviour: a closed web app cannot do much until you open it, which mostly affects notifications rather than speed.
Modern browsers run JavaScript close enough to native speed that a chat interface has no meaningful gap. Scrolling, typing and rendering are all fine.
What differs is what happens when the app is not in front of you. A native app can wake up, sync and hold a connection; a web app relies on push notifications and does its work when opened.
Installing a web app to the home screen closes most of that gap, and on an iPhone it is required for notifications at all.