However, it seems to be out of stock everywhere, and expensive, and i would have thought, given the chip shortages of today,
Surely its not realistic to put this chip on a product?
However, Are there any "climate change sensor" chips on the market?
You'd think there might be, these days
Review the datasheet. BME688 does not measure CO2, it's a kind of estimated CO2 sensor, see https://en.m.wikipedia.org/wiki/Carbon_dioxide_sensor. The commonly used and sufficiently stable method to measure CO2 is IR absorption at 4.26 um. To measure enviromental concentrations (about 0.04 Vol %), you need photometer path lengths of 50 to several 100 mm depending on sensor resolution and stability. The sensor can be hardly implemented on a chip.
While indoor CO2 concentration varies considerably, it's quite stable in outdoor areas and not much affected e.g. by car traffic. In so far I'm not sure about the purpose of your sensor
Measurement of CO2, as an earlier poster has pointed out, is simple in principle. The absorption spectrum has lot of overlap with absorption of H2O and you need to use narrow band interference filters. The detector is special purpose (regular photodiodes do not respond at this long wavelength) but noisy. There is some diurnal variation and seasonal variation on a small scale (if you are taking reading close to an agricultural or industrial field).
To study how climate change is progressing, you need large number of distributed readings over long periods (both space and time) and use some model.
Very little information can be obtained from the readings of an individual sensor at a fixed location over a relatively short time, IMHO.