No you are not dumb. The lazarus installer and toolchain should obey Windows default install paths for executables but it doesn't (Well, lazarus does, but some of the toolchain can't wortk with paths that include spaces.)
This is a known issue and should have been solved years ago.
One way of solving it is to create an empty directory in a path without spaces and create a symlink, junction or hardlink to the path with the spaces that includes the binutils
NTFS only. Although SUBST can be used too
The other way is to add a (about 10 lines of code) LongPathToShortPath utility to pipe the directories in their 8.3 form (both fats and ntfs) before calling out to the utilities that do not support long path names.
Both of these options are tasks for the maintainers. Not your fault.