when starting a video, Safari always expands it to full screen

Try setting up another admin user account to see if the same problem continues. Please post back on whether or not this worked. Also try the Safe Mode. Please post back on whether or not this worked.

Isolating an issue by using another user account 

Safe Mode - About

If it works in the Safe Mode, try running this program when booted normally and then copy and paste the output in a reply. The program was created by Etresoft, a frequent contributor.  Please use copy and paste as screen shots can be hard to read. Click “Share Report” button in the toolbar, select “Copy to Clipboard” and then paste into a reply. This will show what is running on your computer. No personal information is shown. If the log won’t post, try posting it in Pastebin and provide a link in a reply        Pastebin

Etrecheck – System Information

You are welcome. You have so much 3rd party software running, it is hard to guess what is causing the problem. You also have Profile configuration software that may be causing the problem. I suggest you go to System Preferences/Users & Groups and note all your login software. Delete it so you can restart with no open programs running. Restart the computer and do not open any program but Safari. Test to see if it goes full screen automatically. If you still have the same problem, go to System Preferences/Profiles and disable/delete the profiles. Restart and test.