Easiest way for feedback on an X/Y table is like they used for old fuel level sensors, Have a loop of thin wire strung from one end, around the other and back to the start, You could likely even rip apart an old mercedes tubular fuel sender if you just wanted to pinch the entire mechanism so long as you let it soak in a solvent to remove the smell, and run a brasso metal polish rag up and down the wire a few times
The moving head has a double wiper (top and bottom wiper on each wire to ensure good contact) connected across both wires on the loop, you measure the resistance of this loop however you fancy and use that for really basic servo control, probably just using an op amp and you set the position of the servo with PWM or a DAC whatever your preference.
These old things for reference,
https://www.ebay.ie/itm/VDO-dip-tube-sender-279mm-long-for-VDO-fuel-level-gauge-Motorsport-Rally/262101667418?hash=item3d067a0e5a:g:QWAAAOSw5VFWJLBbCan be found at car wreckers for under $5 at most places I have seen, for a reliable linear feedback potentiometer roughly 5-90 ohms. with an end stop contact to boot.
I'm afraid I do not have any internal pictures on hand, But I repair the things for a living (replacing the winding wire and cleaning them out after 20 years of use) so can say they should be fit for purpose. rpeatability on these sensors is quite high,
If you do want to go down the magnetic only path, use a spring to oppose your motion, it helps linearise things quite a lot, you would still probably want to use a length multiplier such as a gear or lever so your solenoid does not have to be bigger than your plotter,