how can we communicate across the two components? Do we have an application event in the lWc framework?
Salesforce introduces Lightning Messaging Service, which allows communication across Aura, Visualforce, LWC. It's a perfect substitution for Application events and it can be used to communicate between different LWC components.
link to documentation about LMS - https://developer.salesforce.com/docs/component-library/documentation/en/lwc/lwc.use_message_channel link to component that you'll use in LWC - https://developer.salesforce.com/docs/component-library/bundle/lightning-message-service/documentation