Of course once again, ChatGPT is wrong.
You say you have an RCCB, which is a residual-current device that detects when the current in L is different from the current in N. That happens e.g. when someone touches L and the current flows thru that person to earth. The RCCB trips and the person stays alive.
For that fault current to flow, there must be a circuit, which is why in the grid, the N is grounded.
With your setup as in your drawing, the L and N of the Multi are floating – no connection to earth anywhere*. So the circuit never closes and the person above stays alive – as long as there is only a single fault. This is called an IT system (see Earthing system - Wikipedia) and it requires isolation fault detection of some kind and is generally only used in special circumstances.
So, long story short, you need to tie N to PE, which is exactely what the ground relay in the Multi does by default.
I think there will be no problem when you turn that relay on, multiple N-PE bonds are only a problem if that is not only the same PE, but also the same N, which it is not in your system (and the worst that can happen with multiple bonds would be nuisance tripping of GFCIs/RCDs/RCCBs).
What you need to think about, however, is where your PEN coming in from the grid is earthed (connected to an earth rod), because if that is outside of your premises, when the grid connection would be cut, there would again be no earth connection and you’re back to an IT system…
Disclaimer: I’m not a licensed electrician, and specifically not licensed by your grid operator or aware of any specific regulations that apply in your location.
*) Actually, there is capacitive coupling through filters, which is why a minimal current flows and lights up your screwdriver.