Full synchronization of computers. How?

Option 1.
You need one carrier. For example, a USB HDD/SSD.
Computers in the BIOS to set to boot from this device.
Enjoy

Option 2.
To use the laptop as the host system. An ordinary computer as a thin client.
Google VNC/RAdmin etc.

Full synchronization
1 takes a long time
2 does not allow to use neither a computer nor a laptop during synchronization.
3 requires an external boot media

Attention to the question
And what for you is happiness necessary?

If you really want to synchronize a set of soft - work for the dev they are transferred much easier

1. To put Virtual Box on both a computer.
2. Create one VM, install OC and the necessary software.
3. To download the hard disk image of this machine to a portable HDD (preferably USB3).
4. Mount image directly from a portable HDD to Virtual Box and run it on the appropriate computer.
5. At the end of the session to write the BackUp image to the computer, in case of loss of the drive.

PS: the Alternative is cloud only, again with a separate dev.

How to sync Windows(10), and the file system (C:, D:) ?

Always work on the laptop. Instead of the PC to use the dock.

Option1:
If we exclude the synchronization of the registry, then you only need any external drive.
Working files and browser profile keep on it, for software search for portable options or put the software on an external drive or store the config there.
OS and software with activation put by default on every computer separately.
Software not easy - you need a specific version of software to be considered separately and explore its capabilities, there is no General solution. But you can usually find an acceptable option.

Option 2: rent a VDS and work there, and your devices to use to access the VDS. However VDS with Windows costs more than Linux, because it is a Windsurfing license to rent.

PS: for the flexibility of always having to pay something