Curiously, I haven't seen any mention of Google Earth Engine (GEE) in these comments so far. On top of offering a massive data repo of optical and SAR satellite imagery dating back to the 70s (LANDSAT 1-9, Sentinel 1-2 and others), it also has a Python API module (and thus can also use GIS, web integration etc.) and you can also use the in-browser JavaScript version (GEE Code Editor) all for free. With that, you can create your own indexes for whatever purpose with some image arithmetics. Its business model is that you have to pay monthly if you're sourcing massive amounts of data or using it at enterprise scale. I think the best part of the JS version (despite being slow at times) is being able to share an entire project with a link.

It seems that Nimbo is trying to offer a more analysis-ready alternative with some pre-processing like cloud removal done beforehand, which can be done yourself with some coding and with greater control on GEE. The lack of mention of the exact spatial or temporal resolution and surface coverage is an odd choice to me. These parameters are what I look for first and foremost when considering alternative data sources. With multiple data products, I think the website should atleast give a range (Minutes, days? Centimeter, meters?) of what resolutions are available. The comparison with Google Earth seen on the website is also bizarre to me as GEE is a more apt comparison because it is specifically meant for manipulating and sourcing satellite imagery. It would be more compelling to see a comparison of that instead.

I previously used GEE at university for flood mapping and mapping forest fire damage. This tool is also actively being used in peer reviewed journals with a large community around it. And yes, you can use it to see the effects of climate change and human impact on nature, I will leave it as an exercise for you to search for examples.