Hello,
Fixed it! at least part of it.
That is how, for those who might have had the same issue:
Why :
1. My logo header is on svg format, with a particular font
2. turns out svg isn’t readable the same way on all devices, especially if you have a specific font that is not a web font. In that case, you might experience a completely different font and even weird spacing missing letters on some devices (mobile in my case)
3. The way I found to fix it is to rework the logo (in illustrator for my part)
How:
1. open the logo in your design software
2. select the whole or part that is problematic
3. in Illustrator, go in “Type > create outlines”
4. Save and export in svg
5. Upload in your WordPress media library
6. Customize your theme so the new “outlined” logo shows in the header.
And voilà!
Hope it wil help some of you.
Now I am left with a size issue that I will open a new topic for, but thank you Lisa for your help and precious advice.