Can't pin extensions to the tool bar (url bar)
Installed Firefox 122 in a new Windows 10 installation and added some extensions (e.g. Gesturefly, Update Scanner, uBlock Origin, Uppity). These pinned fine on my old installation. But I cannot find how to pin them on the new.
All the help I have found Googling, or using search here, says go to the Add-ons Manager page and right-click the extension and use "pin to toolbar". Alternatively click the extension and click the gear icon and use "pin to toolbar". But when I right-click there is no pin to toolbar context menu entry. If I left-click the gear I get "Check for Updates, View Recent Updates, Install Add-on From File, Debug Add-ons, Update Add-ons Automatically, Reset All Add-ons to Update Automatically, Manage Extension Shortcuts". If I right-click the gear I get a line of icons (left, right, reload, star) followed by "Open Image in New Tab, Copy Image Link, Email Image, Save Page As, Select All, View Pate Source, Inspect Accessibility Properties, Inspect (Q)". If I right-click the extension in the Add-ons Manager page itself, I get a very similar list. In no case is there a pin to toolbar option.
How do I pin an extension, given the above? What have I messed up?
Wubrane rozwězanje
What you post in your question is the menu on the about:addons page and not the drop-down panel of the new Extensions button that is placed at the right end of the Navigation Toolbar as you can read in this article.
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Firefox 109 comes with the Extensions button in the Navigation Toolbar as the new way to manage your extensions. The panel that opens if you click the Extensions button (puzzle piece icon) serves as overflow area for extensions you install. The legacy chevron (>>) overflow area still exists but is only used for built-in toolbar buttons as found in the Customize page.
In the Extensions button panel, you can click the gear icon 
next to an extension or use the right-click context menu to pin the extension to the toolbar (Pin to Toolbar).
To (re)move the extension from the toolbar back to the Extensions button panel, you can use "Unpin from Toolbar" in the right-click context menu.
More Information:
The reply from cor-el asks me to do is exactly what I cannot do. The "Pin to Toolbar" and "Unpin from Toolbar" context menus do not exist for me. That is what I reported, in detail, in my original post and question above, and it is because they do not exist that I had to ask this question in the first place. As my post says, I have seen all the advice to click these context menu entries. But for me, the context menu entries are not there: they cannot be clicked. So how do I pin to the toolbar or, perhaps, get the context menus back?
Wubrane rozwězanje
What you post in your question is the menu on the about:addons page and not the drop-down panel of the new Extensions button that is placed at the right end of the Navigation Toolbar as you can read in this article.
Thank you. That made it clear for me -- I sure was dumb. The manage extensions page was the logical place to go, and it had gears and context menus, and I never noticed that jigsaw puzzle button on the toolbar -- I did notice it and focus on it on the manage extensions page. Thanks again for the patience and the clarification that worked for me.
Cor-el / Moderator's "chosen solution" does ultimately provide the solution, however, it does not address the issue of users going to "Manage Your Extensions" (Open Application Menu / Add-ons and themes / Manage Your Extensions) expecting to find "Pin to" or "unpin". The only place I can Pin an extension to the Toolbar is by clicking on the puzzle button which opens "Extensions" and displays my add-ons with a Gear. Clicking on the Gear (Left or Right click) opens the menu to Pin to Toolbar and other options. At the bottom of "Extensions" accessed by clicking the Puzzle is a button labeled "Manage extensions". Thinking . . . I want to manage my extension and Pin it to the Toolbar, clicking it opens up the page "Manage Your Extensions" that allows you to do everything to the extension EXCEPT Pin it to or from the Toolbar.
The point i am trying to make is, Users expect to find "Pin to Toolbar" in 👉Manage Your Extensions and its not there. Maybe one of you under appreciated code writers could add the option Pin to Toolbar to the "Manage Your Extensions" list of extensions three dot ••• menu?
My first reply would be a better description of how the puzzle peace icon works.