Hi @Athulya Pillai ,
Per my test, we are unable to open a spfx webpart in another webpart. we can only connect them with dynamic data like following document
https://learn.microsoft.com/en-us/sharepoint/dev/spfx/dynamic-data
I feel regretful to inform you that it turns out to be a by-design one. As a workaround, I will suggest you to use custom dialog boxes with SharePoint Framework Extensions. You can make a reference to the following document
https://learn.microsoft.com/en-us/sharepoint/dev/spfx/extensions/guidance/using-custom-dialogs-with-spfx
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