I just updated my system and now I cannot find the extensions icon anymore, maybe it has been moved somewhere? I can still enable/disable or upgrade extensions from https://extensions.gnome.org/local/
My experience with GNOME is very limited (frankly, I don’t use it) but with recent GNOME versions, you might have better luck with this, if you’re willing to tolerate flatpaks…
On flathub.org install Matthew Jakeman’s GNOME “Extension Manager”
Can search, or use: https://flathub.org/en/apps/com.mattjakeman.ExtensionManager
Then use this (as an application) rather than browser-based extension management. Let us know if this works for you.
NOTE: I’m not sure but if you don’t already have flatpak capabilities, you may have to enable flatpak repository use, too … as follows:
Install FlatPak
sudo pacman -S flatpak
Visit https://flatpak.org/setup and follow instructions to add flatpak repository (look for EOS emblem from list of distros):
flatpak remote-add --if-not-exists flathub https://dl.flathub.org/repo/flathub.flatpakrepo
Reboot system and flatpak apps should be available (can use sudo reboot now)
It’s also available in the Arch repos as extension-manager
Did not know this… thanks! (In the “extra” repo, no less)
I recommend also using Extension Manager; have used in number of distros and have had no issues. Makes life much easier on Gnome, no hassle with browser connector. 
do you the gnome-extensions-app package installed?
My Extension Icon disappeared as well. Interesting gnome-extensions-app is marked alpha. So I installed extension-manager.
obviously they (finally) changed/replaced the green iconed extension manager with the blue one. the blue one now moved from AUR to extra. So it seems to be the official choice but this needs a manual interaction as the green icon extension manager got removed on update. I needed to “yay extension-manager”, too. A good choice by Arch to replace it.
Solved, thanks
I might be missing something. So I updated to Gnome 51. I saw the Gnome Extension tool disappear. But I saw no instructions to manually or automatically install something else. Nothing on Reddit or archlinux.org. sounds like a bug to me.
Wonder if this would break a new install?