Reproduction steps:
1. Open the “ReproProject“ project
2. Open the “Assets/Scenes/SampleScene“ scene
3. Enter Play Mode
4. Move the mouse somewhere that is not the center in the Game View
5. Click and hold left mouse button
6. Release the left mouse button
7. Observe the Game View

Expected result: The mouse cursor is at the same position it was before clicking the left mouse button
Actual result: The mouse cursor is in the center of the Game View

Reproducible with: 2021.3.37f1, 2022.3.26f1, 2023.2.20f1, 6000.0.0f1

Reproducible on: Windows 11 Pro (22H2)
Not reproducible on: No other environment tested

Workaround: Setting the Cursor.LockState to CursorLockMode.None before changing the mouse position and then setting the Cursor.LockState to CursorLockMode.Confined after the mouse position is already changed