Large storage boxes and trays bigger than the printer's bed, printed in pieces that slide together

Box Maker helps with this. Box Maker is a browser tool that generates a 3D-printable box (3MF, STL or GLB, up to 600 mm, cut into interlocking pieces when it's bigger than the printer's bed) from its outer length, width and height and the wall and floor thickness you choose, with optional rounded corners, compartments (up to 6 × 6, and any neighbours joined into bigger rectangles) and a matching push-on lid.