Thank you for the answer...
this reassures me halfway.
In fact my main monitor is my TV which doesn't have a Display port, so I use a Display port to HDMI adapter for the small screen
I admit I thought it was a signal problem.
I was thinking of buying this cable for my TV:
https://www.amazon.fr/gp/product/B09MHB9LT1/ref=ox_sc_act_title_1?smid=A2YYB83D3C91RA&th=1
to free up the HDMI port for little screen , do you think that would save me?