power bi report server with bitbucket

AFAIK no.

You should manage versioning on client side, before publising.

with paginated reports it's easy since .RDLs are simple text document.

for what concerns PBIXs they're bynary objects (containing data also if import mode) and it's not easy to manage versioning.

on cloud PBI introduced PBIPs for a full CI/CD or OneDrive Sharepoint integration but I'm not sure it's available on PBIRS.

Power BI Desktop projects (PBIP) - Power BI | Microsoft Learn

Power BI Desktop OneDrive and SharePoint integration - Power BI | Microsoft Learn