How do I resize a whole finished project to a different size, and what breaks when I do?

The one-step way

Open Job Setup for the existing job.
Enter the new job size.
In the Design Scaling section, check the option to scale the design with the job size. With it checked, your drawings are resized in proportion and keep the same relative position inside the new material. Left unchecked, the job changes size and the drawings stay as they were.
Click OK, then recalculate every toolpath and reset the preview.

One educator uses this checkbox on double-sided projects such as bowls because it resizes the components and vectors on both sides together.

Use Set Size. Key options:

Link XY keeps width and height in proportion.
Auto Scale Z (3D components): when checked, scaling in X or Y also scales the height in proportion. Uncheck it to keep the Z height constant.
Scale items individually resizes each selected object about its own anchor instead of treating the selection as one group.

Bits do not scale. A detail that a bit fitted into at full size may no longer fit. Run the preview and look for uncut areas.
Material thickness does not scale with the design. Slots, tabs and dog-bone joints sized for plywood must match the real sheet. Remove the fillets, set slot widths to the measured thickness, then add the fillets again.
Holes for hardware or pegs: resizing changes the circles. Either resize the circles back to their true diameter individually, or use the Drilling Toolpath, which drills the center of each closed vector with the drill's own diameter.
Inlays: resize the pocket design only, then recalculate the VCarve Inlay toolpath so the plug is generated again. Scaling both halves by hand invites errors.
Double-sided 3D parts: educators disagree. One scales with the Job Setup checkbox. Another advises against scaling an existing double-sided model and prefers rebuilding it at the new size, because wall thickness changes. Either way, check wall thickness with a cross section before cutting.

Save a copy under a new name before resizing.
To resize one 3D model inside a job and see what height and detail do, see the entry on what changes when you scale a 3D model.
Imported metric models: changing the import size does not change your job setup. Set the job dimensions yourself afterward.