Flathub apps problems

Hi, I have installed the Gnome Extensions plugin in Google Chrome. When visiting extensions.gnome.org, it says native-host-connector not found. Today, I downloaded Free Download Manager and installed its Chrome Extension, but it gives an error saying that FDM is not installed. After some searching, I found that apps downloaded from Flathub have trouble communicating with other apps. Is this true? Is there a way to solve this? Note that both Chrome and FDM are installed from Gnome Software’s flathub repo.

(When I try to install Chrome from Google repo, I get the following error:

package google-chrome-stable-120.0.6099.109-1.x86_64 cannot be verified and repo google-chrome is GPG enabled: /var/cache/PackageKit/39/metadata/google-chrome-39-x86_64/packages/google-chrome-stable-120.0.6099.109-1.x86_64.rpm could not be verified.
/var/cache/PackageKit/39/metadata/google-chrome-39-x86_64/packages/google-chrome-stable-120.0.6099.109-1.x86_64.rpm: digest: SIGNATURE: NOT OK)

That’s a known issue with flatpak web browsers: NativeMessaging portal for sandboxed browsers · Issue #655 · flatpak/xdg-desktop-portal · GitHub

For GNOME Shell Extensions, a good option is Extension Manager on Flathub.

Google broke their repo nearly six months ago when they started using a feature that doesn’t seem to be well-supported. The reports of breakage have been mostly with rpm-ostree and EL7 though. dnf should still work, and I thought PackageKit did too.