I think that will stop Obsidian from automatically showing bakclinks in the note for new notes that are opened.
To hide it in a current note, select the three dots and toggle backlinks in document to hide them.
Vault wide, you might try disabling the backlinks plugin and then quitting and restarting obsidian to see if it toggles all backlinks in notes to off. You can then re-enable the backlinks plugin and use it in the sidebar.