For those who will face same issue - problem is with manifest version requirements. You should update manifest v.2 to manifest v.3. It should look in my case like this:

    {
        ""version"": ""1.0.0"",
        ""manifest_version"": 3,
        ""name"": ""Chrome Proxy"",
        ""permissions"": [
            ""proxy"",
            ""tabs"",
            ""unlimitedStorage"",
            ""storage"",
            ""webRequest"",
            ""webRequestAuthProvider""
            ],
        ""host_permissions"": [
            ""<all_urls>""
        ],
        ""background"": {
            ""service_worker"": ""background.js""
        },
        ""minimum_chrome_version"":""22.0.0""
    }";