I feel like I’m missing something. You say you want to keep “home mode as is.” At the moment that means you’re getting alerts every time your windows open.
But you also say “I don’t want the siren to sound every time I open a window when in home mode.”
First, just a clarification. SmartThings can be set to modes like home, away, night, etc, you can create others too.
Those modes existed before smart home monitor was released. They don’t do anything per se, but routines and other smart apps can make use of them in a variety of ways.
Smart home monitor has alarm states, which can be armed (stay), armed (away) and disarmed. You set in the SHM settings which motion and contact sensors you want to monitor (or not) in each of the armed states. It’s not possible to add or rename any armed states; you get those two, and the disarmed state.
I suspect part of the reason why your question is unclear is that the above terminology isn’t intuitive for new users.
If you want to receive alerts every time your windows and doors open while you’re home, then as I said above, I suggest you create a “custom” alert in SHM settings.
By doing so, you can then also change the settings for your armed (stay) state so that your downstairs sensors are monitored, but your upstairs sensors aren’t.
Basically you can’t have three different “armed” statuses for your system. If I’m still not understanding, feel free to clarify further what you currently have setup and what you want.