Where your saved videos are
Videos you save in iCap appear on the folder tab at the bottom of the screen, one folder per video.
They are not added to the Photos app automatically
Videos are stored in folders inside the app, so they don't show up in Photos on their own. To move one there, open it and choose "Save Video" from the share button.
Videos saved as HLS can't be exported
If you chose "Keep as HLS" when saving, the video is stored in an iOS-specific format (.movpkg) that can't be taken out of the app. If you want to watch it in other apps or on a computer, choose "Convert to mp4 (recommended)" instead.
Getting them onto a computer
The same folders are visible in the iPhone Files app under "On My iPhone" → the app's name, and you can copy them elsewhere from there. This works even if the app won't start.
See also Where did that feature go?