Here is my config.json:
{ \"env\": \"dev\", \"dev\": { \"projects\" : { \"prj1\": { \"dependencies\": {},
The jq program .dev.projects."$v" in your example will literally try to find a key named "$v". Try the following instead:
.dev.projects."$v"
"$v"
jq --arg v "$PRJNAME" '.dev.projects[$v]' config.json