[FIX] web: keep the search options visibility state

The search buttons visibility is saved in the local storage. Rev.
6448420c changed the API of the LocalStorage servive (by JSON
parsing the values), and didn't adapt the calls done for the
search buttons.

Closes #33833

closes odoo/odoo#34206

Signed-off-by: VincentSchippefilt <VincentSchippefilt@users.noreply.github.com>