I am connecting from my home pc to Windows Server via RDP.
Theoretically speaking, if the remote server is compromised, can it somehow automatically infect my home pc?
No file transfers, only clipboard sharing, default RDP options.
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Short answer - highly unlikely, but not impossible.
It depends on the infection vector of the virus. The virus can only spread if it is able to run code on your home pc.
If it uses a vulnerability to spread (e.g. like a worm), your home pc must expose this vulnerability to the infected system. Based on your description, you are worried, that the infection takes place specifically over the RDP protocol. In this case the RDP client on your home pc must be vulnerable. If your software is up to date, there is currently no such vulnerability known in the RDP client. You always have a residual risk of a 0-day vulnerability, but I would consider it highly unlikely that a virus is using such a 0-day and no one has identified this behavior yet.
The second infection vector is actually transferring virus code to your home pc via RDP and running it locally. This could happen for example, if you copy the malicious code and either run it yourself or it gets executed somehow by your operating system. Therefore, if you copy something malicious via clipboard sharing to your system, be careful how you treat the data you receive that way. Since you do not specify what you actually want to do over RDP (e.g. salvage some important data from the infected system), it is hard to say how risky your activities will be. If you copy data from the system, be sure you know what you are doing.
I recommend using a throw-away operating system to access the infected machine, if you really have to. Something like an isolated virtual machine that you delete afterwards or an OS that you are willing to wipe after you are done.