Eurogamer did a very in depth review of Cloud vs Digital (with physical as a footnote) impact on the environment.
https://www.eurogamer.net/articles/2021-10-13-gaming-downloads-climate-crisis
Summary:
- Physical is as bad as downloading 128GB or more worth of data.
If you only install a game once (and none so far are 128GB or more) then it's better to buy digital.
However, with pro consoles, BC (if it doesn't download the full game anyway), cross-gen, deleting to make room, sharing and the second-hand market it's not that clear cut.
- Digital downloads are better depending on time played.
It's about 10GB per 2 hours play time. If you play more, digital download is better. Play less, streaming is better for the environment.
Of course there are other factors with streaming. Streaming is not very efficient if you do it on your console or desktop. They still use all the power, might as well render it all locally. Thin power saving clients are best for streaming.
Oh and one example, playing the same game on Switch vs high end desktop, factor 1:20 difference in eco footprint.
Rest mode and patches are bad. Consoles constantly keeping a vast library of downloaded games up to date cost a lot of extra power. Best to decide what to play before downloading a whole bunch and try a little here and there. And only patch what you want to play.