Hello , some good news : I did a swap of SSD between 2 macbook air
The first is a Macbook air 7,2 13p and has a boot rom version of 427 : I took his Apple SSD and re-installed Big Sur with the sintech + NVME drive, TimeMachine etc.. all is working on it, no fan noise, no sleep problems, no high temperature, the NVME gives me 1460 mb/sec in speedtest read, about 1100 in write. Are those numbers good ? It seems that the MBA is more responsive.
So for the MacBook 6,1 11p where Mojave couldn't be installed directly : I have put the apple 128 Gb SSD in it, reboot , USB installation of El Capitan : no firmware update, Sierra : nothing, Sierra security update : HOLY COW , TAdaaaaam : boot rom was something more recent. Mojave installation with AFPS conversion : OK, Mojave update... all is working. Big Sur installation after that : 100% working and now I have a very recent boot rom : 431.
I would like to say thank you for your assistance, and also to 2 others people here.