The gimbal does a fantastic job of keeping the image stable.

Does the added weight of a filter noticeably reduce the gimbals ability to do its job?

I know that an ND filter is probably only a gram but if nothing else it will put the cameras out of balance slightly.

Gimbals always work best when the camera is perfectly balanced.

Does the camera have optical stabilisation or is it purely the gimbal that keeps the image steady?

It's only the gimbal and the heavier the filter, the more work the gimbal has to do.
On larger cameras with interchangeable lenses, you often have to balance the camera.

As long as you get a light weight filter and put it on correctly, you should be fine and notice no difference.

I have successfully used filters on my Mavic Pro for years. When I got my Mini 2 I ordered a set of Freewell ND filters. Very well made, feather light and easy to attach solidly. However, unfortunately it causes slight vibration in the video much of the time that is no doubt caused by the filter. It is very noticeable and renders the footage useless. Really unfortunate.

I have ordered the Freewell Bright Day set.
I hope mine does not vibrate :-/