Such a cool project :D
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Very interesting! Thank you for sharing your project!!
However, in terms of some of the benefits you mention in the "motivations", bandwidth, energy efficiency and CO2 might weak points: after all your server (backend) stays on 24/7 and it does all the heavy lifting anyway, doesn't it? So you are not really saving bandwidth/energy/CO2... (unless - of course - you cache in "time" and "space" and reuse the search results for queries of yours and of other users).
Yes, I didn't research this extensively... it was more of a hunch. :D Yes, certainly, I simply thought that if you minimize phone usage, it would result in a longer battery life and fewer charging cycles, which in turn would reduce CO2 emissions... but I admit it's a bit of a stretch. :D
In a similar spirit, there used to be an app called SMSmart that can proxy your phone's internet connection through a vpn tunnel over... SMS! So if you don't have any internet connection but has unlimited sms plan, you could still access the internet, slowly. I bet your webapp would pair very well with this.