You cannot just copy system files to a new computer and expect to have a well functioning operating system. Part of the installation involves hardware detection, and configuration as a function of the hardware. Also, do not expect that simply copying files of a more recent OS version over an older version will not lead to a successfull upgrade.
You can copy system files and use the copy to restore the operating system on the same computer to a previous "state". That is what the utility "Time Shift" is designed for.
For this to work, the system files need to be copied maintaining all their attributes, including preserving hardlinks if any. Accordingly, the files must be copied to a file system that supports linux permissions. Alternatively, the files and their permissions could be stored in a tar archive. The tar archive, which will be several gigabytes in size, can then be stored on Google Drive if you want so. To make it more managable, you can, also with tar, create incremental archives.
This will cost you a lot of efforts. On a personal note, I encourage you to do these efforts only provided you have a good backup system in place for your personal files. If not, then first dedicate your efforts to the latter. Personal files are unique in the world. Once lost, they are lost forever. An operating system can be downloaded anytime, and is installed in less than an hour. Far less effort than that required setting up a system backup. This, of course, provided that we are talking about a personal computer here. Keeping a data server up and maintaining it is another matter.