"A Backup all your graphs" export button for www.desmos.com using TamperMonkey / GreaseMonkey / etc. Save it as a Json file, and opens it in a new browser tab for verification.
Navigate to the main calculator page of Desmos.com, wait for the button "Backup all graphs" to appear in the top-right corner of the page. If it is disabled, you should just need to update the view e.g. by dragging it a bit with the mouse. Click on the button to save all your graphs as a json file. It is also displayed in a new tab for verification or copy-paste.
Once you have installed TamperMonkey/GreaseMonkey/variant plugin in your favorite browser, then it's as for any script: click on the name.user.js file above, then "raw". Tampermonkey should then directly propose to install the script, otherwise click on your Monkey plugin icon shortcut and manually copy-paste the code as a new script.
It is my second script ever :-D ( I followed the model of DesmosToSVG ) and the hearth is from MathEnthusiast314 ; it is tested [TODO] only on Chrome and Firefox. I hope all will go well for you as well ! ;-)
Many tricks on the DesmosGraph unofficial blog - comprising a list of others plugins and scripts.