I have disabled the button tooltip and it was working fine till March 2022 update.
In April 2022 update, the option name slightly changed as below
As you can see it is off. But when I publish the report, tooltips are enabled. In edit mode, I can see the options are old and No Tooltip is off. Hence it is showing the default tooltip. Kindly fix this bug.
I turned off the Tooltip in Desktop as you said, and then published the report to the Desktop. I saw on the Service that the Tooltip of this report was also turned off. My Desktop is also the April version.