In my test, boolean values were displayed correctly in both desktop and service.
What is the data source? How did you calculate boolean values? What is your desktop version? If viewing reports with a different web browser, does this problem occur?
Please provide more detailed repro steps so that I can check for you. If possible, please share your .pbix file, remember to mask sensitive data before uploading.
I had this issue too and took me forever to figure it, but Desktop treats true/false values in a column with data type of "Any" differently. I had CALCULATE measure in Desktop that had something like where [Column of Interest] = "TRUE" that gave me the result I was looking for in Desktop, but was blank when I published it to the cloud. That column has a lot of values besides true/false so I didn't think twice about leaving the column type as Any. To workaround it, I changed the column type to "text" in PowerQuery. It was certainly BEYOND FRUSTRATING to have that treated as two different things across Power BI