Merge JSON Files via Bash or JQ

I've go files containing compressed JSONs. All JSONs having the same root fragments "id" and "test":

file1.json:
{"test":{"a":2},"id":"850303847"}
{"test":{"a":3},"id":"2742540872"}
{"test":{"a":4},"id":"1358887220"}

file2.json:
{"test":{"b":3},"id":"850303847"}
{"test":{"b":3},"id":"2742540872"}
{"test":{"b":4},"id":"1358887220"}

file3.json
{"test":{"c":8},"id":"850303847"}
{"test":{"c":4},"id":"2742540872"}
{"test":{"c":5},"id":"1358887220"}

I would like to merge these Files based on it's IDs resulting to:

{"test":{"a":2,"b":3,"c":8},"id":"850303847"}
{"test":{"a":3,"b":3,"c":4},"id":"2742540872"}
{"test":{"a":4,"b":4,"c":5},"id":"1358887220"}

I've looked into jq -s option for this but fail to find a way. Any ideas how to achieve in Bash (with or without JQ)?

You could reduce all inputs into an object with .id as key, deep-merge using *, then iterate over the fields .[] to obtain a stream again (use the -c flag for compact output):

jq -nc 'reduce inputs as $i ({}; .[$i.id] |= (. // {}) * $i) | .[]' file*.json

{"test":{"a":2,"b":3,"c":8},"id":"850303847"}
{"test":{"a":3,"b":3,"c":4},"id":"2742540872"}
{"test":{"a":4,"b":4,"c":5},"id":"1358887220"}

Demo

Here is one way:

jq -nc '
reduce inputs as {$test, $id} ({};
  .[$id] += $test
)
| keys_unsorted[] as $id
| {test: .[$id], $id}' files...

^{Online demo}