Are there a mode like hibernate but still run server in Windows? (or any OS) [duplicate]

If you want a small server to run while your main server is off, I would suggest something like a Raspberry Pi and run it off that

What you are trying to do sounds pretty much impossible to me

No, you cannot hibernate a computer without actually hibernating it.

Hibernation stores the entire state of the system to disk. Included in that hibernation is the state of devices, the disk and a lot of other stuff.

If you leave the computer running for any time after writing the final bytes to disk then changes will happen to the disk and system that do not match up with the state saved in the hibernation file.

The result is that the hibernation file is immediately invalid but assumed to be correct. As a result it may restore the system and use an old version of filesystem tables that are no longer correct and so (in the best case) simply drop changes that may have happened to the disk since it was hibernated and at worst result in corruption.

If your system disk is slow then you might want to look into replacing an HDD with an SDD which can improve boot times.

You may also want to look into small dedicated machines to act as servers.