You should be able to fix this without reinstalling the system.
Please share the output of “ls -l /usr/bin/*”
Can you login with root user and root password, like with “su -” ? If not, you would need to boot with a live iso and mount your “/” filesystem there to fix it.
If all you did was change the ownership, switch to a TTY, login as root and run:
chown -R root /usr/bin
That isn’t a particularly good idea in general but given the state of your system it shouldn’t make things worse. In my system, everything inside /bin is owned by root.
In general, if you have a tutorial/guide/person telling you to change permissions in /bin, find a different one. You should never need to do that.
Don’t change permissions and owners on files installed by the package manager, not even on aur packages. It could make your system vulnerable, not a big deal on personal computers, but on servers it can be really bad. Most of the times you need to add your user to a group that owns the files in the package to use it.