How to add dependencies into package.json with jq

I want to add package dependencies to the package.json file by bash script using jq.

Add new element to existing JSON array with jq

Here is the test script with 5 steps:

#!/bin/bashadd_element_with_jq() {    # step 1: Add a new root element "{}" first    echo "============= step 1 ================"    echo "{}" > "package.json"    # step 2: Add a "dependencies" sub element to the root element "{}"    echo "============= step 2 ================"    # step 3: Add a "foo" package with version "1.1.1" to the "dependencies"    echo "============= step 3 ================"    jq '. += dependencies {"foo": "1.1.1"    }'"package.json"    echo "=========== step 3 output =================="    cat "package.json"    # step 4: Add a "bar" package with version "2.2.2" to the "dependencies"    echo "============= step 4 ================"    jq '.dependencies += "bar": "2.2.2"'"package.json"    # step 5: If the "foo" package already existed, then update to the latest version. Otherwise, add the "foo" package to the dependencies.    echo "============= step 5 ================"    jq '.dependencies += "foo": "3.3.3"'"package.json"    echo "=========== final output =================="    cat "package.json"}add_element_with_jq

Here is the error:

============= step 1 ============================= step 2 ============================= step 3 ================jq: error: syntax error, unexpected '{', expecting $end (Unix shell quoting issues?) at <top-level>, line 1:. += dependencies {                  jq: 1 compile error=========== step 3 output =================={}============= step 4 ================jq: error: syntax error, unexpected ':', expecting $end (Unix shell quoting issues?) at <top-level>, line 2:"bar": "2.2.2"           jq: 1 compile error============= step 5 ================jq: error: syntax error, unexpected ':', expecting $end (Unix shell quoting issues?) at <top-level>, line 2:"foo": "3.3.3"           jq: 1 compile error=========== final output =================={}

Here is the expected output:

=========== step 3 output =================={"dependencies": {"foo": "1.1.1"  }}=========== final output =================={"dependencies": {"foo": "3.3.3","bar": "2.2.2"  }}

What's wrong in my bash function, and how to fix the jq commands?