If Photos cannot play a video

There are several possible reasons, why a video cannot play - Photos may not be compatible with the codec of the video, Photos may not be able to access the video, if it is missing or there are problems with the file ownership or permissions, the video may be damaged or stored on an incompatible volume, or it cannot be downloaded from iCloud because of network problems or lack of storage.

• The system version on your Mac matters, because the upgrade to macOS 10.15 Catalina removed some 32-bit system frameworks, that are needed to handle videos in an older legacy format. Some videos you imported before the the Catalina upgrade may now be causing problems and should have been converted to a more compatible format before upgrading to macOS 10.15 Catalina or later. This list for iMovie might give you an idea what to look for: About legacy media in iMovie for macOS - Apple Support
• The location of your Photos Library matters: If your library is on an external volume, this needs to be prepared as described here, orPhotos may no longer work properly: Move your Photos library to save space on your Mac - Apple Support . Make sure the file system format of the external volume is MacOS Extended(Journaled) or APFS and not case-sensitive. Otherwise Photos may not be able to find the resource fork of videos in a container format, like MOV. The drive needs a wired connection, don't use a network share, and the volume must not have been used for Time Machine backups or have other backup software installed.
• Check the codecs of your videos. After the upgrade to Catalina or later, I would stick with HEVC or H.264. You can see the codec of your videos in the Info in Photos, when you select a video.
• If you are using iCloud Photos: The free storage storage matters, in iCloud and on your Mac. iCloud will no longer work properly, if you are running out of storage in iCloud, and you may not be able to view the videos, if you do not have enough local storage to download the video from iCloud.

See also: If a media file doesn't open or play on your Mac, iPhone, or iPad - Apple Support

More user tips for Photos: Thematic Index to Photos for Mac related User Tips… - Apple Community