I believe the OP only has a single monitor. And depending on the age of the laptop, thunderbolt may not be an option. But there are KVMs that share one monitor, one keyboard, one mouse between two PCs without requiring thunderbolt. The VRR issue aside of course....
As for your second monitor, you'll either have to connect it to only one PC or manually switch between them. You could use two different inputs to the monitor, one from each computer and just cycle them.
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