Variable variables won't process the array key, or arrow operators, like you've tried. You could do what you're trying to do by using eval(), but don't :P

However, json_decode accepts a flag to return an associative array rather than stdClass objects. https://www.php.net/manual/en/function.json-decode.php

$foo = json_decode($json, true);

Once you have that, you could get the value you want by using a function to resolve an array value by dot notation, which can be stored as a variable. See this answer: https://stackoverflow.com/a/14706302/2286736

<?php

$json = '[{
    "date": "2019-07-04T10:21:15",
    "title": {
        "rendered": "Wisconsin Investment Board"
    }
}]';

// decode as associative array
$pmdd_ds_json_obj = json_decode($json, true);

/**
 * @link https://stackoverflow.com/a/14706302/2286736
 */
function resolve(array $a, $path, $default = null) {
    $current = $a;
    $p = strtok($path, '.');

    while ($p !== false) {
        if (!isset($current[$p])) {
            return $default;
        }
        $current = $current[$p];
        $p = strtok('.');
    }

    return $current;
}

// key variable
$key = '0.title.rendered';

// value can be resolved by the dot notation path
$value = resolve($pmdd_ds_json_obj, $key);
var_dump($value); // Wisconsin Investment Board

Additional changes to the resolve() function to allow it to accept objects as well:

$json = '[{
    "date": "2019-07-04T10:21:15",
    "title": {
        "rendered": "Wisconsin Investment Board"
    },
    "_links": {
        "self": [{
            "href": "https:\/\/refi.global\/europe\/wp-json\/wp\/v2\/posts\/309891"
        }]
    }
}]';

// decode as normal (with stdClass)
$pmdd_ds_json_obj = json_decode($json);

function resolve($a, $path, $default = null) {
    $current = $a;
    $p = strtok($path, '.');

    while ($p !== false) {
        if (
            (is_array($current) && !isset($current[$p]))
            || (is_object($current) && !isset($current->$p))
        ) {
            return $default;
        }
        $current = is_array($current) ? $current[$p] : $current->$p;
        $p = strtok('.');
    }

    return $current;
}

// key variable
$key = '0._links.self.0.href';

// value can be resolved by the dot notation path
$value = resolve($pmdd_ds_json_obj, $key);