iOS 12 introduced new restrictions for devices that have mobile device management (MDM) profiles installed. Go to iOS Settings > General > Profiles to check if you have an MDM profile installed. If you do, you can check to see if you have the specific restriction listed: "Opening documents from managed to unmanaged apps not allowed".
By default, any device running iOS 12 that has an MDM profile with the above restriction installed will not be able to share managed calendars with Fantastical (or any other third-party apps that use iOS's Calendar data).
To resolve this, you will need to speak with your workplace's administrator, who will be able to grant Fantastical the necessary clearance it needs to access your managed calendars.
Specifically, Fantastical either needs to be added as a managed app in the MDM profile, which allows it to access iOS's calendar data, or the "Opening documents from managed to unmanaged apps not allowed" restriction needs to be removed from the MDM profile.
It takes a few minutes for your iPhone to transfer the updated app to your Apple Watch after updating. Wait 5-10 minutes before trying to use Fantastical on your Apple Watch after updating. If Fantastical still doesn't open after waiting 5-10 minutes, restart your Apple Watch and try again.
If Fantastical says it doesn't have access on your Apple Watch, please try the following:
Fantastical can only show reminders that will be due soon when you are not near your iPhone. Reminders that are due soon will be shown, but you will not be able to see reminders without a due date or reminders that are due in the past or far in the future.
Apple Watch only allows a small amount of data to be sent from your iPhone to your watch. Because of this, Fantastical on Apple Watch may not be able to show events too far into the future and instead keeps you informed of events that are more likely to be relevant to you.
This is due to a bug in watchOS.
To fix this, launch the Fantastical watch app and then hold the watch's side button until the 'Power off' option appears. When this appears, hold down the digital crown for a few seconds to force close the app.
After re-launching Fantastical the complication should work as expected.