In your situation, i would use a "current work" LR catalog on the laptop (should work nice&fast on a SSD), and after finishing a project, export the catalog on the NAS, then import it to the full catalog which is also stored on the NAS. This is a bit flimsy, but as far as I can tell, adobe has not yet implemented something to automate this process.
There are, in fact, various solutions to automate this procedure. The choice of software that mirrors hard drives (or individual folders) is huge, some using the cloud, some doing it directly. That takes care of the type of backing up as you suggest it without requiring any manual work. I find this a most secure solution since it normally also allows you to directly get a copy off-site.
You talk about general backup solutions. This is not what i mean, because a huge 100k pictures LR catalog does not fit on a 500GB drive
I would like to have in lightroom an option to "relocate" old stuff to a NAS without kicking it out of the catalog, but that is currently not easy to achieve - working with two catalogs is much easier. I also heard that a small catalog works fater.
Of course, you could create for every project a new catalog and then just copy it over to backup - but then you can't browse "all" your work.
Another point: physical separation of the backup: a second backup (single disc acceptable) which is at your workplace/parents/friend can be handy when something comes like sandy