I think I can comfort you with a statement on the website of Apple:
Time Machine automatically backs up your entire Mac, including system
files, applications, accounts, preferences, email messages, music,
photos, movies, and documents. But what makes Time Machine different
from other backup applications is that it not only keeps a spare copy
of every file, it remembers how your system looked on any given day—so
you can revisit your Mac as it appeared in the past.
On the given page, there are even tutorials on how to restore your Mac from a Time Machine copy.
Please be aware those backups are not bootable. So you still have to manually install a fresh OS (from USB, DVD or other...)