In a form view of a project.project model, I display related calendar.event records through a one2many field as a kanban

I'd like to filter that kanban view, but it doesn't work as described below.

On the form, I added the following field:

<field name="event_ids" mode="kanban"/>

The kanban shows up nicely on the form. Actually, a kanban view has been applied by default: the one that has the lowest sequence id.

As the system selected a kanban view, I assumed a search view is also applied by default.

The search view with the lowest sequence id is the following:

<record model="ir.ui.view" id="view_calendar_event_mysearch">

     <field name="name">calendar.event.mysearch</field>

     <field name="model">calendar.event</field>

     <field name="arch" type="xml">

        <search string="My search view">

            <field name="allday"/>

            <filter string="Full day events" name="filter_on_fullday" domain="[('allday','=',True)]"/>

         </search>

     </field>

</record>

If the search view would have been called from an action, I could have indicated a default filter in the act_window, like:

<field name="context">{'search_default_filter_on_fullday': 1}</field>

which made me think I could define a context on the field, like:

<field name="event_ids" mode="kanban" context="{'search_default_filter_on_fullday': 1}"/>

I must be missing something in my reasoning, because it doesn't work.

Maybe, no search view is selected by default. Can someone confirm?

How can I force a search view? And once a search view is applied, would it use the default filter?

If there is a search view, how can I tell the search view to execute the filter?

Thank you for your help.