SDI Cookie is not being saved

I was trying to add Sling Dynamic Include (SDI) in a component that is set cookie in the browser.
Before SDI Enable:

+ The Dispatcher cache was disabled.

+ Each time the page is refreshed, the component Model class is rendered and set cookie in the browser.

After Enable SDI:
+ Dispatcher cache is enabled and the page is being cached.

+ Also enabled the SDI so the component is not being cached. (I checked the corresponding HTML code from the dispatcher cache it's working. The component is not being cached.) Also, I checked the server log, the Model log is also written in the publish server.

+ But the cookie is not set in the browser.

Why this happened? Or what could be the possible solution or mistake?

My OSGI Config

{
    "include-filter.config.enabled":true,
    "include-filter.config.path":"/content",
    "include-filter.config.resource-types":[
        "my-project/components/content/meta-navigation",
        "my-project/components/content/lms-survey"
    ],
    "include-filter.config.include-type":"SSI",
    "include-filter.config.add_comment":true,
    "include-filter.config.selector":"nocache",
    "include-filter.config.required_header":"Server-Agent=Communique-Dispatcher",
    "include-filter.config.appendSuffix": true
}