I don’t have any experience with seagrass, sisal or jute but I did install a solid bamboo floor in my flat which I was very pleased with. As I’m sure you know, bamboo is far more sustainable than hardwood floor because of the rate it grows compard to wood whilst still being incredibly strong. Personally I chose strand-woven bamboo planks with click-lock tongoue and groove which makes them very easy to install (once you’ve cut all the fiddly shapes aroudn the doors and walls) and looks very similar to light oak to the untrained eye. They were pre-laquered to make them hardwearing and waterproof. I don’t have specific environmental information on the laquer but the bulk of the material is bamboo, and wood still needs protection.
If you want to go with wood but with an environmentally friendly covering and are prepared for a bit more upkeep you could try a soap finish which is quite popular here in Denmark and gives a light untreated look. This is as simple as it sounds: a soap flake and water solution rubbed over the bare wood from which the soap is left behind once the water has evaporated. Note that as it is just soap so it will wear off and consequently you will have to maintain it every fortnight to every month, depending on how much use it gets. For this reason it is a more common finish for furniture. Perhaps a slightly more practical solution is natural oiled floor which lasts longer between maintenance. With the right care both these solutions will last decades.
You’ll find loads by googling “soap finish” but here’s some inspiration and detailed tips on how to care for your floor