If I try to catch a PDF on a web page through the webclipper, it returns this error:
"The Joplin extension is not available on this tab due to: Missing host permission for the tab"
I checked also on the GitHub issues back to 2022 that reported as solved but not working. Not working also on the PDF files reported on the tests of GitHub
Do you mean that you are trying to clip a PDF which is being displayed on its own in a Firefox tab?
If so, from what I have found this permissions message is a Firefox issue not a Joplin one and there's a bugzilla report going back about 6 years relating to it.
It appears that this is actually by design and a relevant quote says,
...the viewer is treated as part of the browser, meaning the viewer (including the rendered PDF) becomes a privileged page that extensions cannot modify.
So it seems that the web clipper is not allowed access to the tab because as far as Mozilla is concerned the rendered PDF it is not a web page, it is part of Firefox and so protected from extensions. So you therefore get the message, "The Joplin extension is not available on this tab due to: Missing host permission for the tab".
However even if the webclipper could access the tab I am not sure it could clip what is actually a PDF and not an HTML web page.
No. This is how Mozilla has designed Firefox to work.
Mozilla has prevented extensions from accessing a PDF displayed using Firefox's inbuilt PDF viewer. That is by design. However what is being displayed is not a web page it is a PDF. So even if Mozilla did "fix" it and allow extensions I doubt that a web-clipper would work with a PDF, even though it is being displayed in a web browser tab, as it is a PDF not a web page.