Welcome to the forum (both of you)!
You may need to take an extra step to install some of the fonts, which don't copy over. For the fonts which did not install when you tried to copy/paste, try this. Copy/paste the missing fonts, but do not paste into the fonts directory. I use the Documents library for saving font files. Open the font file (double-click). That will produce a small window with an Install button. Just click that, and it will install the font.
Once all the fonts are actually installed, Inskcape will show them.
Actually it was the new computer, rather than the new Inkscape version, which is the culprit here. You simply don't have all the fonts installed on the new computer, which you had installed on the old one. But as I said, once you have the fonts actually installed, Inkscape can use them.