How to implement PUSH notifications when the Google Chrome browser is closed?

Question

Google Chrome

Good afternoon, please tell me if there is any possibility to raise some kind of push notification server or something similar offline Intranet to implement push notifications to computer users on the Intranet using the Google Chrome browser (even when closed)
Namely, on the Intranet deployed everywhere as a standard Google Chrome browser, there are also many self-written applications on the network, many computers on the network are thin clients, where, roughly speaking, the user is running only a browser on Linux OS (also Google Chrome)
So the task is to give application developers the ability to send PUSH notifications to users who have subscribed to them
I don’t really understand these technologies, but as I understand it, at least some special extension for chrome is needed here (as well as a checkmark in the chrome settings that does not completely close the browser if there are running extensions), because. by default, if chrome is closed, then it will no longer send any push notifications)
And perhaps you need to raise some kind of push notification server of your own?
Tell me please