Can we show team chat on SharePoint

poka1234 Check below SPFx web part sample which might help you with your web part development.

This is not the exact functionality you are looking for but you can refer the source code which will help you with your web part development: Current User's MS Teams and send message 

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poka1234 there's no out of the box web part but you might be able to build a custom one with SPFx.

Rob
Los Gallardos
Microsoft Power Automate Community Super User