Lancet report https://www.thelancet.com/journals/lancet/article/PIIS0140-6736(21)02724-0/fulltext

persistent urban myth that green sputum means you have a chest infection that needs antibiotics
not the case.
Special rules if you have serious lung condition eg cystic fibrosis or COPD, but for people who are otherwise well, green sputum does not = a need for antibiotics.  https://systematicreviewsjournal.biomedcentral.com/articles/10.1186/s13643-021-01767-6 and https://erj.ersjournals.com/content/39/6/1354)
the colour can’t distinguish between viral and bacterial infection illness https://www.ncbi.nlm.nih.gov/labs/pmc/articles/PMC3410464/

and NICE don’t use it as a means of differentiating the use of antibiotics or not https://cks.nice.org.uk/topics/chest-infections-adult/management/acute-bronchitis/ – it really is a holistic assessment judging how ill the person is and how ill they were to start with

– the question isn’t usually ‘is this bacterial or viral’ but more ‘what are the chances this person will benefit more from antibiotics than not’. A lot of bacterial infections will only get better marginally faster with antibiotics, and with all the side effect costs.
Below from 1952 shared with me on twitter –

https://www.thelancet.com/journals/lancet/article/PIIS0140-6736(52)90988-4/fulltext

more on mucus

https://erj.ersjournals.com/content/39/6/1354

NICE guidance https://cks.nice.org.uk/topics/chest-infections-adult/management/acute-bronchitis/

https://www.ncbi.nlm.nih.gov/labs/pmc/articles/PMC5640107/

Honey! systematic review https://ebm.bmj.com/content/26/2/57