How to make browser notifications that will works without Internet?

I understand what you asked for. I gave you an alternative option, which you don’t have to use.

This tells me two things: you might be open to alternatives, and that you are making assumptions.

What research have you done?

Here’s a lead: WTH is there no Home Assistant app for Windows - #11 by SeanM. I’m not saying this answers your requirement to not make use of the Internet for notifications but maybe it gets you somewhere.