On the online sever that where your game save is stored and with all your settings.
I don't think that is true.
The "game save" (progress data and settings information) is stored on your PS4. You can, with an account that has a PS+ subscription, upload it to the
Sony online storage like any game but that is
completely independent of PD/GTS.
If you were to uninstall GTS
and then delete your game save from your PS4,
and then re-install GTS, your game save is not pulled back down from the GTS servers because its not on the GTS servers. You've then effectively got a day-zero GTS installation... unless you've uploaded your game save to the
Sony online storage and can then download it again from there.
I don't think that GTS even sends a copy of your game save to the GTS servers, for their game save "tampering" check, at all and there is no circumstances that I can even imagine it doing so, as that would be horribly inefficient and completely unnecessary waste of network bandwidth, storage and money.
For example, the game save data for my GTS installation is ~250mb. If every GTS player - and last time I saw there were ~9m unique installs/players - had a similarly sized game save then that would require 2,250,000 gigabytes of storage alone (enough to fill 2,250 1-terabyte drives), the network bandwidth to receive that lot would be even more, and there would be quite a large bill for the data centre and equipment to go along with it. Yes, I know, that would probably be small change compared to the costs associated with the
Sony online storage but that is PS+ service paid for by every PS+ subscriber. The difference is that the
Sony online storage
needs an entire copy of your save game (otherwise it wouldn't be much use!) whereas, for a simple "tamper" check, PD does not.
I suspect GTS will use what is referred to as a "Hash" or "Checksum".
A hash/checksum is a (usually*) unique hexadecimal string, generated from a set of data, that is much (much!) smaller than the original data but can be used to check the validity of the original data. And by smaller I don't even mean megabytes, or even kilobytes, but bytes.
For example, this is the MD5 hash of the Windows installer for version 2.93.3 of the Blender 3D software, as published on the Blender website: e8a406e22ecebeeea84c996e56f1d67f
If I were to download that same installer and feed that into an MD5 generator app, it would generate a Hash based on that installer file. If the Hash generated by the app matches the Hash published on the Blender website, for that particular installer, then I know the installer hasn't been tampered with and its safe to use it to install Blender on my computer.
Similarly, whenever the annoying "saving" box pops up on screen in GTS, rather than wastefully sending your entire game save data, GTS will look at your PS4's unique ID and your game save data, generate a much smaller hash derived from said information and send
that hash to the GTS servers. Then, when you next start up GTS, and it performs its tamper check, it will again generate the Hash, only this time, it will check that Hash against the last one sent to the GTS servers and if it doesn't match then it knows that, at some point, the save data has been tampered with (and will do whatever its supposed to do in such circumstances).
* Somtimes the same "unique" number can be generated for two completely different sets of data (called a "collision") but this is, more often than not, usually down to a poor implementation of the algorithm used to generate the hash. (Its often far more complex than that really, but thats the general gist of it).