https://data.worldbank.org/indicator/EG.USE.COMM.GD.PP.KD
https://data.worldbank.org/indicator/SP.POP.GROW?locations=XD-1W
https://data.worldbank.org/indicator/EN.ATM.CO2E.PP.GD
https://en.wikipedia.org/wiki/Projections_of_population_growth#Growth_regions
https://www.sciencedirect.com/science/article/pii/S2096511718300069
https://www.wsj.com/articles/the-worlds-resources-arent-running-out-1398469459
~Energy usage per dollar of value produced is going down, i.e. wealth can increase without further use of resources.
~World population growth is going down, and is currently nearly static in high and middle income countries (it would actually be negative without immigration, looking at birth rates; nearly the entire first and second world are below replacement fertility rates). https://en.wikipedia.org/wiki/List_of_sovereign_states_and_dependencies_by_total_fertility_rate#Country_ranking_by_Intergovernmental_organizations
~CO2 emissions per dollar of value produced is going down.
~Going by current market trends and how increasingly cheap and economical alternative energy sources are becoming thanks to private and public research and investment, renewable energy is projected to make up 71% of world electricity generation capacity by 2050. The difference will mostly be solar and wind eating into coal's share, as the latter will soon no longer be competitive in the market.
-Going by current demographic projections, world population will peak in 2100 and then decline.
-In the past few years, renewable energy has actually become cheaper per unit energy than oil, and it's only getting cheaper.
Also, Ross, if someone tells you that socialism can save the environment, immediately ignore everything they say from then on. Socialist regimes are far, far more wasteful than equivalently rich capitalist regimes, objectively and statistically, and no useful green technology has ever been developed in them due to lack of incentives.
https://en.wikipedia.org/wiki/Environmental_issues_in_Russia
The destruction of the Aral Sea, the rapid deforestation (RUSSIA is running low on trees to this day), the extinction of whales, the rampant pollution, Chernobyl, etc. were hallmarks of Soviet environmental policy. Furthermore, here is energy use per dollar of value produced in 1990-1991, the twilight of the USSR:
Pollution per dollar of value produced at the same time:
The World Bank data for 1992 (just a year after the dissolution of the USSR, therefore the ex-USSR's economies shouldn't be totally unrecognizable yet) has Russia/Ukraine/Belarus/Kazakhstan at ~x2.5 the U.S.'s emissions per dollar and nearly x4 the EU's or Japan's. Check any other ex-socialist country at the earliest point data is available (usually 1992, just a year or two after socialism fell) and you can see how awful they all were.
It wasn't just the socialists in eastern Europe and central Asia, nor was it limited to the 20th century. Cuba, probably the last socialist nation remaining (besides North Korea, which doesn't have a lot of data available, and Venezuela, which is a petrostate), emits nearly three times as much CO2 per dollar of GDP as comparably poor Latin American countries like Guatemala and El Salvador. It even emits more than vastly wealthier nations like the Dominican Republic.
This is actually due to the exact opposite reasoning of what you said in your "island" scenario; rather than everyone deciding production via market signals, as happens in a market economy, production is decided at the top by central planning, resulting in quotas that have to be met even if the products are literally thrown into the trash (as happened with the USSR's eradication of whales). If some bureaucrat says that they need to produce X cars or harvest Y whales, it happens, regardless of whether that's actually going to be benefit anyone, much less be sustainable. There is also no real mechanism for scarcity to be effectively and subtly communicated in a socialist economy (as opposed to a capitalist one, where the prices will progressively go up, thus encouraging slow easing on consumption or developing substitutes) because prices are totally arbitrary due to being subject to government change at a whim.