Sorry to correct the narrative here, but there was no suitable venue or facility local to Birmingham, and there wasn't enough time to organise an alternative.
Just one of those things it seems.
The CGF officially announced on 13 August 2019 that due to infrastructure and logistics issues shooting had to be excluded and a proposal to add archery was rejected .
In January 2020, the Indian Olympic Association (IOA), which functions also as the CGA representing India, submitted a proposal to the CGF to host a combined archery and shooting championships in Chandigarh during January 2022. The proposal was endorsed by the National Rifle Association of India (NRAI), the Government of India, the ISSF and WA.
The CGF Executive Board approved the proposal at their meeting in London which took place on 21–23 February 2020, and also confirmed that the '2022 Commonwealth Shooting and Archery Championships' and the '2022 Commonwealth Games' (Birmingham 2022) will be two separately organised and funded Commonwealth Sport events.
The CGF proposed to issue a medal table one week following the Birmingham 2022 closing ceremony that includes results from Chandigarh 2022 as a further and final ranking of competing nations and territories from the respective competitions.
In July 2021, the CGF announced that the 2022 Commonwealth Shooting and Archery Championships event in Chandigarh had been cancelled due to the COVID-19 pandemic in India.