Your point is absolutely correct and as far as I can tell you pointed it out genuinely, not facetiously. Edit: read other later posts here: didn’t know about the bacteria part. Learned something today!
This is absolutely not my area of expertise but intuitively there are two categories of energy sources: one which releases co2 (or other climate change impacting gases) and one which doesn’t. Wood, oil, gas, coal falls into the former. It’s just a question of time as you say until the loop closes. Solar, wind, thermal, etc would fall into the latter as far as I can tell.