I'm currently considering buying a PS5 because, if you look at the current graphics card prices, the price-performance ratio is extremely good and with around 10 teraflops of power and an extremely fast SSD you will probably be well equipped for the next few years. The PS5 supports 120FPS in games such as Cod: Cold war, Rainbow Six Siege, etc.
Would it then make sense to get a 144hz monitor, even if you only have 120FPS or 60FPS? Or may the picture even jerk if you have less FPS than Hertz?
I think it's worth it. The PS5 will not produce the frames in a completely regular basis. Of course, more than 120fps would be better.
In principle, 144Hz at 120 / 60fps do not offer any advantage, but of course you are more flexible with the screen for the future.
If the refresh rate of the monitor deviates significantly from the frame rate, this can lead to stuttering and tearing, to avoid this you have to make sure that Vsync is activated in-game.
I also think I have read that the PS5 supports AMD Freesync. If your monitor is also freesync capable, 144Hz with 120 / 60fps should generally not be a problem.
P.S. I'm a PC-only gamer and have no experience with consoles. Technically, however, the same rules should apply as for PC gaming.
I recently switched from 60hz to 144hz and can say that it's really comfortable. However, I play on the PC and therefore have faster movements where you can tell. Still, I would say there's a noticeable difference.