So I am getting the mouse position by interpolating based on last_state and current_state.... but the mouse "feels" laggy (it is smooth though).

Try to decouple the mouse movement from the rendering. The mouse movement is in direct control of the user and any lag will be really obviously. Therefor I would sugguest to render always the current position of the mouse (no interpolation).

Still there is one issue you need to address. When the mouse interacts with your game, in other words, the mouse interacts with rendered content like buttons, then you need to synchronize this interaction with the rendered content. Eg when the user press a mouse button, you need to consider what was rendered at this moment on the screen at the mouse position, this is most likely an interpolation of your last and current frame.

Another way is to split your updates into two categories: fixed step and variable step, or in Unity terms FixedUpdate() and Update().

Objects that are governed by the fixed step update would be interpolated, while the rest (particles, UI for example) would update every frame with a variable step, then render their latest state.

When the mouse also affects visible player character orientation (3rd person game) you'd need to override the player orientation in between fixed steps, so that there's no sync issues between camera / player character.