Good afternoon The_Train_Enthusiast,
We'd like to help with the issue you are having with video playback on your MacBook Air. What is the model year for this computer? See > About This Mac. We ask, because updating the computer to macOS 13.4 would be one of the first troubleshooting steps to address this issue.
It sounds like you are asking about video when streaming, not playing back video files that are stored on your computer, is that right? If so, the next step would be to check the speed of your network. Are you using Wi-Fi or are you connected via an Ethernet cable to your modem/router? (A wired connection is much, much faster.) What is the download speed on your network?
Try quitting Safari and shutting down the computer.
Then, unplug the power to your modem/router (if a single unit), wait for a minute, and plug the modem and router back in. Wait till the status lights are green, and then turn on your Mac and open Safari. Check the network speed again and see if a previously opened website and video plays any better after "recycling the power" to the network.
Let us know the results and we'll go from there.
If Safari doesn't open a page or work as expected on your Mac
Take care.