Keeper.sh now connects iCloud, Fastmail and any other calendar that speaks CalDAV, the open standard for calendar access. Google and Outlook sign in directly, and CalDAV covers the Apple calendar on your phone and services such as Fastmail.
Connecting takes your address and an app password: a separate credential you generate for one application and can revoke on its own, without changing the password you sign in with. The connect dialog links to the page where iCloud and Fastmail issue app passwords.
A connected CalDAV calendar works like any other. Keeper.sh reads it on a schedule, sends its busy time to your other calendars, and can write into it as a destination. Any server that follows the standard works, including Nextcloud and Radicale.
What each calendar service asks for lists the details iCloud, Fastmail and CalDAV servers need.