Missing Internal FCPx Effects?

There may be a problem with the system if those effects are missing. Please post an EtreCheck report  https://etrecheck.com  giving the application full disk access in System  Preferences. When it finishes the scan, click Share Report and choose "Copy Report.” Use the Additional Text button to paste the report into the reply.

I'm assuming you never went into the application bundle itself to install or do anything with effects.

Move the application to the trash, but don't empty it. Log into the App Store and download the application from the Account Purchased page. Do this AFTER Chrome and it's garbage has been removed. Don't reinstall Chrome. Use Safari or Firefox. There are other Google based browsers that supposedly work, but I'm not that trusting.

https://chromeisbad.com

  [Loaded] com.google.keystone.daemon.plist (Google, Inc. - installed 2021-08-23)
[Loaded] com.google.keystone.agent.plist (Google, Inc. - installed 2021-08-23)
  [Loaded] com.google.keystone.xpcservice.plist (Google, Inc. - installed 2021-08-23)
Top Processes Snapshot by Energy Use:
  Process (count) Energy (0-100) (Source - Location)
  Google Chrome Helper (Renderer) (23) 14 (Google, Inc.)
  WindowServer 12 (Apple)
  Google Chrome 4 (Google, Inc.)
  Google Chrome Helper (GPU) 3 (Google, Inc.)
  bluetoothaudiod 2 (Apple)

Your system doesn't have a lot of resources, and it appears it might be damaged by Chrome's malignant behavior. You should use the instructions on the website above to completely remove Chrome, and its keystone daemons (and anything Googke related while your at it), and then reinstall the application from the App Store to get the effects back.

Chrome loads keystone, which basically runs continuously looking for updates. This is a completely BS operation, but that's the kind of thing Google does. When Chrome and other applications run they will swamp the video toolbox and other system functions, breaking them for other applications. The particular effects and transitions you're using rely on the system rather than prebuilt effects. At some point it's likely to happen again, especially on an underpowered system.

Just to confirm you installed the plugins in the Motion Templates folder in Movies, is that right?

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It will probably break again on your system.