A cheap option is one of these sainsmart 6 axis robot arms: https://www.amazon.ca/gp/product/B00UMOSQCI.
I haven't documented anything yet, but I got the arm working with ROS/MoveIt! for kinematics. The code is here: https://github.com/lukeinator42/sainsmart_arm_ros. It uses cheap servos though so I don't think the accuracy is near 0.25mm.
Here's a video that shows the arm in action: https://www.youtube.com/watch?v=Yi_QydaN-34
I'm currently also building a Roboteurs RBX1 Remix arm that uses stepper motors, but it's not complete yet.
Annin AR3 https://www.anninrobotics.com/
Original software for it is a bit hard to work with, improvements in https://github.com/ongdexter/ar3_core
Have a look at https://shop.elephantrobotics.com/products/mycobot-pi-worlds.... If you really need better repeatability, they have a more expensive Pro model.
There's plenty of Pi projects, here's one article https://robotbuildingkit.com/the-6-best-raspberry-pi-robot-a...
Check out the 3d printable esp32 robot arm at https://www.20sffactory.com/
idk about anything specific or anything recommended here. but thought I'd share my thought: I've seen one on kickstarter about 2 years ago. not sure the name but it seemed very practical.
My personal experience with two different robotic arms (< $500) and some additional research is the lack of high level software and libraries, which is quite crippling as it’s very complex to control.
If you’re not used to control theory and inverse dynamics it’s quite tricky to control it (especially at 0.25mm) and you’ll never get to actually use it to perform what you want.
You might have better luck with low-end industrial robots but the cheapest are $2500 and more.
(I’m similarly in the market if a product can prove me wrong, especially interested in something with some computer vision integration)