Depends on specific machine setup and how good the backup is.
Backup requirements for /usr there are sticky bits set on some binaries. That needs to be preserved. In all cases soft links likely need to be preserved for things to work correctly on future package installs. Hard links can be problematic, but if you have a large enough drive or not that many it wont matter. Running package verification can be help after restore to make sure everything looks right. If running a Linux system with SELinux in enforcing mode (RHEL on many derivatives), then the security context will also need to be preserved BUT running a relabel will probably work if the security context was not included in backups. Sometimes running the relabel process wont work if there are files that needs a specific security context but are not listed in the security context database. Can’t provide more details because most of my experience with that is on systems we just replace (LSPP custom labeling resulted in systems that if you booted into permissive would then be unbootable, so they were just reinstalled once any debugging was done).
For /boot things can get tricky depending on the distribution, what boot manager is used, and /boot was a separate partition or not. Basically the boot manager (probably grub) needs to know how to find the files in boot so it can load the kernel. In most cases if you restore /boot and rerun the tools to update the boot manger everything will be fine. BUT some distributions, hardware setups, or dual boot configurations are more complicated, so extra work might be needed.
You didn’t mention /dev, which is all special files. These don’t need to be restored, just make sure the right processes recreate them. There are tools to do this, hopefully the packages are installed. Or boot from a rescue disk and fix it. Look up instruction for your specific distro.
CEC (technically I think displayport could support it, but generally isn’t implemented) and ethernet up to 100Mbps.