ideas for creating linear movement/ general suggestions for approach please

lax123:
but idk about that pair of bellows, how to "drive" it and about its "fixed" volume with its flexible parts.

To drive it you would just need to push or pull the two sides together, easily done with a mechanical linkage operated by a servo.

I'd expect the displacement to be consistent, if not very predictable. If consistency does prove to be a problem I expect you could improve it by enclosing the bellows. I'd have thought this was much easier to build than something capable of generating enough force to operate a syringe - I'm envisaging something that takes significant force in both directions, and needs to be positioned accurately.