This will be system dependent, but it's very much a thing. Vsync means "vertical sync." Rendering and drawing are separate processes. Frames are rendered in the GPU, but they are then drawn to a screen, pixel-by-pixel, from the top of the screen to the bottom. Normally, it is possible to render frames faster than they can actually be drawn.
If vertical sync is ON, then it will take significantly longer for every frame to be drawn. This creates a much more "solid" looking image, but it does impact FPS. Vsync attemps to draw at the screen's native refresh rate. So, if my refresh rate is set to 120 Hz, then the screen will attempt to draw complete images, from the top of the screen to the bottom of the screen, 120 times per second. If for whatever reason it can't maintain that FPS, it will draw at half of that refresh rate, so 60 FPS. If the GPU can't maintain that, it will drop by half again to 30 FPS. This "switch" can happen multiple times within a few seconds, and the additional frames, even though they were rendered are not actually drawn.
^ This is why mouse movements feel like they are "lagging". It's not a sensation of 1:1 movement because the GPU can't actually draw the frames quickly enough.
if vertical sync is OFF, the GPU will now render and draw partial frames. It will take, depending on the GPU, the drivers, the game, and the type of approach being utilized, anywhere from 4 to 16 pieces of various frames presently rendered in the video buffer and just draw that "strip" of the frame to the screen. This is, obviously, much faster, but it will result in whole-screen images appearing "misaligned". What people refer to as "screen tearing". This is why technology like G-Sync an Freesync are popular options, as they will use methods of better aligning the torn strips and creating images with far less screen tearing, all while gaining the additional FPS and responsiveness possible while vsync is off.
The key to dealing with mouse lag is (as is almost always the case) balance. The goal is to figure out how many FPS your GPU and monitor are actually consistently capable of drawing. Adding a frame cap with vsync ON to ensure that the screen draw never falls too far behind will alleviate the issue, though the max FPS may be way below what many players want. Conversely, you can disable vsync, but I still recommend a frame cap, as it's very often possible for GPUs to be generating far more frames than can ever be used. That just cooks your card and wastes electricity for no benefit. A screen can never draw more FPS than it's refresh rate. Any frames rendered beyond that will simply be dropped. And for a game like Cyberpunk, it's very unlikely that anyone will be able to consistently maintain more than 120 FPS, even with top-of-the-line hardware.
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Or, in brief, to alleviate mouse lag:
1.) With vsync ON, cap your frames to something below your average FPS in-game.
2.) Disable vsync, and cap your frames to your refresh rate or half-refresh rate.
