The "standard" and recommended approach from IPCC 2021 has net zero impacts of biogenic CO2 uptake and emission. It is a somewhat safe approach where one can assume that any biogenic carbon ends up in the atmosphere anyway at one point, so the net impact from uptake and emission is zero. This results in a characterisation factor of zero for "carbon dioxide, non-fossil" and for "carbon dioxide, in air", which is excluded from the characterisation factors and not shown in the impact category (we usually exclude characterisation factors that are zero). Maybe, at least for CO2, we could include the zero values into the characterisation factor tables to highlight there that these values are zero on purpose and not missing.
You are mentioning the ecoinvent implementation of IPCC 2021, which is only compatible with the ecoinvent database and where the biogenic carbon dioxide is set to zero correctly. You can even find the ecoinvent implementation (mapping) here:
https://github.com/ecoinvent/lcia/blob/master/3.10/methods_mapped/IPCC%202021_mapped_3.10.csv
You can include biogenic carbon by adding all elementary flows "Carbon dioxide, non-fossil" with +1, "Carbon dioxide, in air" with -1, "Carbon dioxide, non-fossil, resource correction" with -1 and changing all "Methane, non-fossil" from 27.0 to 29.8, which is similar to the EN15804 based on EF 3.1 and using IPCC 2021 for climate change categories.
But be aware that when the full life cycle is modelled and there is no significant carbon sink that lasts for several thousand years there should be (theoretically) no difference between tracking biogenic CO2 uptake/emissions (-1/+1) or putting it to net zero (0/0). But the risk is that explicitly tracking biogenic carbon uptake and emission can lead to unjustified claims of carbon credits or low carbon footprints due to the advantageous carbon uptakes in incomplete cradle-to-gate LCAs with no subsequent modelled release back into the atmosphere.
