[REF] web_editor: remove unused variable

The `hasSearch` variable on `this` was not used anywhere and, if it was,
its semantic was arguable because it was set true as soon as the search
was fired rather than when the search had returned.

I'm taking this opportunity to use async/await as it's *way* better here.

closes odoo/odoo#92014

Signed-off-by: Romain Derie (rde) <rde@odoo.com>