Hello SneevCo,
To help resolve the issue where videos using Safari aren't playing on the Linkedin website, clear the cache and history in Safari by following the steps from Clear your browsing history in Safari on Mac:
1. In the Safari app on your Mac, choose History > Clear History, then click the pop-up menu.
2. Choose how far back you want your browsing history cleared.
To clear cache, select the Develop menu in the Safari app and then choose Empty Caches. If you don’t see the Develop option, open the Safari menu [top-right] in the app and choose Preferences. Select the Advanced tab in the Preferences window. Next, check the box beside Show Develop menu in menu bar option. You will now see the Develop menu option.
Next, follow the steps here: If Safari on Mac doesn't open a webpage or isn’t working as expected
Best Regards.