Privacy

Short version: there is no "us". This is a page in your browser, not a service with a database.

What's remembered, and where

Your home town, recent places, units, chosen activities, custom activities, your indoor temperature and panel size are kept in your browser's local storage so you don't have to type them again. They never leave your device and you can clear them any time from your browser settings. This storage exists only to do what you asked, so there is no consent banner to click.
No cookies are set. No analytics. No advertising. Nothing is sent to this site's host when you use the page — the page is static.

When you look up a place, the town name goes to Open-Meteo's geocoder and the coordinates go to Open-Meteo (forecast, air, sea level, archive), the US National Weather Service (alerts), OSRM (drive time from your home) and CelesTrak (ISS orbit). That's what a forecast needs.
If you tap the pin, your browser asks you first; if you allow it, your coordinates are used for the lookups above and sent once to a reverse-geocoder to turn them into a town name.
Those services have their own privacy policies and see your IP address, as any website you visit does.

When you share a window, the link contains the place, activity and duration so the other person sees the same thing. It contains nothing about you.

The page is its own source — view source and you can see every request it makes.