omniToolkitAPI can be used to set Omni-Channel Status from Button using Lightning Aura Component in Salesforce.

Sample Code:

Aura component:

<aura:component implements="flexipage:availableForAllPageTypes" access="global" >
    <lightning:omniToolkitAPI aura:id="omniToolkitId" />
    <lightning:card>
        <lightning:button
                          label="All Channels"
                          onclick="{!c.setOmniChannelStatus}"
                          variant="brand"
                          aura:id="All">
        </lightning:button>
        <lightning:button
                          label="Break"
                          onclick="{!c.setOmniChannelStatus}"
                          variant="brand"
                          aura:id="Break">
        </lightning:button>
    </lightning:card>
</aura:component>

JavaScript Controller:

( {
    setOmniChannelStatus: function( component, event, helper ) {
        
        let strButtonLabel = event.getSource().getLocalId();
        let objOmniToolKit = component.find( "omniToolkitId" );
        console.log( 'Button clicked is ', strButtonLabel );
        let strStatusId = strButtonLabel == "All" ? "0N58c000000092H" : "0N58c00000007A2";
        objOmniToolKit.setServicePresenceStatus( { statusId: strStatusId } )
        .then( function( result ) {
            console.log( "Result from set status", JSON.stringify( result ) );
        }).catch(function( error ) {
            console.log( "Error in set status", JSON.stringify( error ) ) ;
        });
        
    }
    
} )

Output: