"But after the expiry the Ark server could claim the funds and sweep them"

What does this mean? Will the vtxos be automatically converted to my onchain balance if the wallet loses internet connection for 24 hours and fails to refresh them? Will I only lose the fees?

It means that the server has access to your funds. In theory it could steal it, if it had malicious intent. This is why it’s important to refresh your vtxos. For the signet version, the vtxo expiry is set to just a day, but for a mainnet system, we are thinking about 1 or 2 months.

In practice, in the current implementation, nothing happens. You can still use and refresh the vtxos in the Ark even though the actual money on-chain has already been swept by the server.

In the future, what we expect will happen is that the server will automatically re-issue vtxos when a user forgot to refresh them before expiry. This way the server is never in control of any actual user funds because expired vtxos are immediately re-created.