Question about HP Omen 25

V-Sync: Vertical synchronisation
Prevents image data from changing while the screen is still building up the image. This depends on the driver and the graphics card. However, today's graphics cards almost all support this.

G-Sync: Nvidia proprietary technology which the screen and the graphics card must support.
Freesync: Open standard from AMD (but not supported by Nvidia cards) which must also be supported by the graphics card and the monitor.

All three techniques are intended to prevent or at least reduce artefacts (so-called tearing) during fast movements in games.
If G-Sync or Freesync is in use, V-Sync can be deactivated, as V-Sync then no longer brings any additional advantage.
If neither can be used, V-Sync is the last option to minimise tearing, but it costs performance.

You must mean Freesync, and yes, that makes a difference with your 1050, Freesync doesn't work with it!

No, that makes no difference for V-Sync, as this is software-based. Or do you mean G-Sync?