The jq program .dev.projects."$v" in your example will literally try to find a key named "$v". Try the following instead:
jq --arg v "$PRJNAME" '.dev.projects[$v]' config.json
The jq program .dev.projects."$v" in your example will literally try to find a key named "$v". Try the following instead:
jq --arg v "$PRJNAME" '.dev.projects[$v]' config.json