If I understand, the overall CO2 (and weighted N2O, CH3 equivalents) net balance of of in home vermicomposting (or other composting) is at the crux of the question here.
Some rigorous and easily repeatable testing of the compost vs vermicultivation has been done, the results put vermicomposting as in improvement in general; and that CO2 and CH3 reduction performance could be improved with the sufficient inclusion of carbonaceous material, aka 'Brown' and also improves with increasing density of worms.
It seems than any net CO2 (N2H, NOx , H2S, plastic nanoparticles) discussion could include the net effects of the total emissions caused by transportation systems for large scale collection of wastes. Simply not adding to that source of emissions makes some sense in reducing net CO2 and other equivalents. Whatever that amount is, zero is less than any.
Then, in the case of the resulting fertilizer from on-site vermicomposting, there is the potential for further net reductions by not purchasing or transporting fertilizer to your garden; however small that might be. Add to that the further reduction in transportation of the vegetables costing only the breath walking from garden to kitchen. Truly, this isn't a facetious argument; the net total of all CO2 from consumer produce shipping is made up of exactly all our little bits we didn't grow or gather ourselves, and by conservative estimates most produce contributes an average of 0.1kg of CO2 equivalent per 1.0 kg of food due to transportation of that food.
a comprehensive meta-analysis of 1530 studies, supplemented
with additional data received from 139 authors, assessed against
11 criteria designed to standardize methodology, resulting in 570
suitable studies with a median reference year of 2010.
The data set covers ~38,700 commercially viable farms in 119
countries and 40 products representing ~90% of global protein
and calorie consumption'.
One reference for actual numbers comparing composting to worms:
Vermicomposting as a technology for reducing nitrogen
losses and greenhouse gas emissions from small-scale composting
As all food waste byproduct not incinterated will eventually undergo decomposition, whether intentional or simply buried in a landfill; any situation which worms participate in the process appears to reduce harmful emissions overall.
In both composing cases; at home or collected/municipal; the total food waste emissions might change in rate of release vs duration of decay, but not in aggregate total emissions. So, it would appear that little net difference in direct emissions is made if none, any, or all homes compost. As the ratio of vermicomposting is used to replace composting; the specific emissions should decrease as shown.
Any reduction of transportation related emissions in the pursuit of a transition from composting to vermicultivation appears to be a tangental but beneficial outcome. In some specific situation where the transition would increase the distance, total net mass, or utilize dirtier energy sources this might work against those gains.
TLDR; Vermicomposting reduces nitrogen loss 10–20% over composting,
decreasing N2O 25–36% and methane emissions by 22–26% and may be less overall when including transportation related CO2 and other greenhouse emissions.
So, if forced to choose worms or composting, the worms are marginally better overall. If the total volume of food waste was handled at home; compost or vermiculture, the reduction in transportation is the same, and reduced emissions would occur to the extent that worms are preferred over compost.