Then it really shouldn't be a browser app, it needs to be a local app that runs in the taskbar.
I've made two of these in the past:
V1, browser based: the browser simply wasn't viable because there's no taskbar timer.
V2, Bash+zenity script to run locally, pops up a uncloseable, uncoverable and omnipresent (across all workspaces) window, with a progress bar showing the time as it elapses[1], and properly sends desktop notifications. A much more functional experience than V1 which was invisible while I was working, stuck on a single workspace (I have nine in a 3x3 grid) and frequently didn't send notifications.
V3, Next iteration, local application without a window but with taskbar integration for timer display. Might just decide to hack zenity to provide a 'taskbar' widget.
[1] If you're interested my V2 app (run locally), see https://gist.github.com/lelanthran/bbbcf5c8b6b26c9bc0263384a...