We do not define position of yandex 'native' controls. You can use ymaps api for that.
Or it may be possible via css.
And easier would be to change position of leaflet control.
To put search control over markers - special handling needed - see Yandex.addon.Controls.js.
Firstly, it has a strange position. At what layer it is? How can I drive it's sizing?
While searching something even only one time I'm always getting the next error