Summary

This magnetic base chess set is based on...
DUCHAMP Chess Set by jacky3131 on Thingiverse:
https://www.thingiverse.com/thing:4854758

I redesigned the rook to make it resemble the other pieces more closely.
Rather than trying to insert magnets into the board, which would require aligning the magnetic poles with those in the chess pieces, I used a thin steel plate as a base for the board. By doing so, I didn't have to orient the magnets in the chess pieces in any particular polarity.
12" X 12" 16 Gauge Mild Metal Steel Sheet Plate
https://www.amazon.com/dp/B0FJDHDVVT

On the bottom of the plate, I attached a felt pad using 2" double-sided tape...
12" x 12" 1mm Thick Felt Paper
https://www.amazon.com/dp/B0CQN64JTW

2" wide double-sided tape...
https://www.amazon.com/dp/B08GQ9F86X

For the board itself, I modified this board...
Puzzle Chess Board - Remix by TeamOliva on Thingiverse:
https://www.thingiverse.com/thing:3092069

I didn't like the border, so I modified 3 pieces to make them edge pieces. I also resized them to 40mm square and thinned them to 1.5mm thick to allow the magnets to attach better to the steel plate under the board.
I attached the chess board squares to the steel plate using five or six large drops of thick CA glue each, and then used 2" wide blue painters tape to hold the piece in place while the glue dried.
The thick CA glue sets fast, so you don't have a lot of time to position the square.
This is the CA glue I use on my projects...
https://www.amazon.com/dp/B0C3BM9878

The width of the board is 320mm, which means it overhangs the 12" plate by approximately 7mm on all four sides. You could resize the board squares to make a perfect fit, but I liked the shadow line created by the overhang, so I didn't.

For the 64 magnets ( 32 X 2 ), I used these...
12mm X 3mm round magnets
https://www.amazon.com/dp/B0CCXJQJNF

A single magnet per piece was not strong enough to hold the piece securely to the board, so I used two magnets each. I applied a large drop of thick CA glue to each chess piece and a small drop of CA glue between the two magnets.