Methane is going to come out of sewage whether we process it or not, and methane itself is a greenhouse gas. It's not going to come out of the ground without help (in the quantities we are using).
... it's incredibly potent as CH4... and then it "breaks down" into CO2 and H2O.
I think enkid's point is agreeing with you: might as well burn that sewage CH4 for energy-- you end up with the same CO2 in the end and less CH4 in the atmosphere in the short term.
And the gas comes from biowaste, which is actually nice, because municipalities which have the most effective ways of collecting and processing biowaste can export the resulting biogas to e.g. surrounding municipalities and in this way generate income to run things for everyone.
This means waste must be sorted somehow, but this is a rational thing to do anyways.
And it pisses me off immensely to see some idiots throw plastic bags or non-food waste to the biowaste bins. There are signs in many languages and even with pictures, but some people still manage. Such biowaste cannot be used for gas generation, so it's kind of hurting all the inhabitants.
According to VafabMiljö [1], who runs the local biogas facility, in the year 2020 they processed 16157 tons of household biowaste, i.e. 66% of entire processing that year. The other stuff was sewage sludge and slurry from packaged/unpackaged food items (total of 8246 tons).
16157 tons of household biowaste turned into gas to run buses with and not dumped into a landfill is a good thing.
In 2012 the municipality collected 60% of overall food waste to turn it into biogas. Back then they hoped to reach 80% eventually. [2]
I didn't find newer collection numbers (they are somewhere, I just stopped iterating), but the number can only be higher today.
[1] https://www.vafabmiljo.se
[2] Naturvårdsverket rapport 6518, September 2012 (ISBN 978-91-620-6518-8).