We are using Internal CSS and it is working fine but after upgrading to version 5.6.6 it is not working.
we have tried to reproduce at your site but it is working fine over there.
As you have mentioned that you are not able to reproduce this in our online examples, we will need a small runnable test so we can debug it and assist you with a solution by looking at what is wrong. We can't say anything without looking at the code.
Any reason why you don't just use your application's own CSS file?
I have created a generic LWC in SF and others can use it. So they need to pass their column config to this generic component. In column config they are passing their own tooltip desings.
This code used to work because we used to set tooltip html with innerHTML property. But recently we switched to DOMParser().parseHTML() which is patched by LWS and does not allow <style> tag. You can use a workaround to get old code working, you just need to return DomConfig object instead of string: