The workspace is stopped; its files stay.
Pick a session on the list, or start a chat. On a wide screen, "Beside" opens a session next to the others, up to four; the lines between them drag. A question Claude asks waits for your answer, in its chat and under Needs you.
Every session runs in your workspace in the cloud, a machine of its own on Fly with the repositories you cloned there: not on your computer, and not in the Claude app. Closing this page leaves it running. The amounts beside a chat ("est.") are Claude Code's own estimates at API prices, not a bill: signed in with a Claude plan, you pay the plan, not each token.
To speak instead of typing: the microphone beside a chat's field, where your browser offers one, types what you say for you to read and send. Your browser's own speech service does the listening (Apple's in Safari, Google's in Chrome), not Proofpane. Your keyboard's own dictation works here too.
A chat's Connectors (MCP) lists the servers it has: a repository's own, from its .mcp.json, run only once you approve them there, each as it is shown (a changed one asks again); the ones you add there, and your Claude account's connectors, run as Claude Code runs them.