Pi-hole not working network-wide

Yes.
Both tools target a different area.

Pi-hole does suppress DNS answers for unwanted domain names and will do so for any DNS request from your network, regardless whether that has been issued by an OS, browser, app, IoT appliance or any other source. Being centrally managed, it can do so even while your clients are oblivious of Pi-hole's presence.

A browser extension does only filter traffic from your browser and has to be installed on every device in every browser you are using.
But it allows fine-grained control of filtering below domain level, e.g. blocking certain images or scripts. Trying to filter such content with Pi-hole would almost certainly result in overblocking, precluding you from wanted as well as unwanted content.

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