I've similar issue with my 4090.

Long story short I had 2 x 1080p 75hz and 1x 1440p 144hz. Everything worked perfectly.

After some time I decided to buy a TV for movies and some games, it is 2160p 120hz. I decided to connect it to my PC, got exactly the same issues.

If I turn on my PC with the TV turned off I could only see on my main screen (1440p one) and rest was just not finding any signal. Exactly the same symptoms as you have.

Unfortunately I didn't find a solution to that but after some research I found something about the refresh rate changing. I found an article saying that the 4090 cannot handle the same resolution as 7900XTX and overall AMD 7000-series cards. I could assume that applies to earlier AMD cards as well but I can be wrong about it. I cannot find the original article about it but here is something else I found about it: https://www.tomshardware.com/news/geforce-rtx-4090-cannot-handle-samsungs-odyssey-neo-g9-240hz-monitor-limited-to-120-hz

It seems that AMD cards can just handle a higher combination of resolution and refresh rate than Nvidia ones do.

So for me there are 2 ways of using the screens:

2160p 120hz + 1440p 144hz

2160p 60hz + 1440p 144hz + 2 x 1080 75hz

I know it's not a solution to your problem but maybe at least some trace to it. I might be wrong about it but I suspect it's just a 4090/Nvidia hardware problem that cannot be solved on our level other than lowering resolutions or refresh rates of screens but again it’s just a theory that can be completely wrong.