I mean you could also just buy whatever case you want from the secondhand market place. I bet that is much more sustainable than to buy one that is completely new.
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If you’re looking for a case made with sustainable materials you can get a Pela Case or Apple FineWoven (I have a FineWoven case and it’s held up really well). The thing with either of those is that I don’t think they’ll last 4-5 years.
I think there is a strong argument to be made for a durable case because reducing your consumption is also eco-friendly. Additionally buying something strong and durable reduces the likelihood that you’ll have to replace your phone if you drop it! Strong and durable category you can consider Caudabe (from my experience, really solid cases).
I had an “eco-friendly” case before and it fell apart within a year, I now have a regular one and it looks almost brand new after nearly 2 years of use. If you ask me you will be causing more environmental damage by constantly buying new cases rather than getting one to last.