Spine determines the video resolution by calculating the largest size needed to display the entire animation. However, there is currently no direct way to obtain this calculated size without actually exporting the MOV file. The size is based on the content within your project, and Spine uses this to ensure the entire animation fits within the video. If you need to know the size beforehand, you might consider using a placeholder or guide within your project to estimate the dimensions.

Export calculates the size, as Spinebot mentioned, by checking the bounds at each frame that would be exported and using the maximal bounds from that. The editor doesn't provide a way to calculate that, except by seeing it on the export dialog.

You could calculate it by writing some runtime code. Here is an example that poses the skeleton and prints bone information. You would calculate the maximal bounds instead.
EsotericSoftware/spine-runtimesblob/4.2/spine-libgdx/spine-libgdx-tests/src/com/esotericsoftware/spine/BonePlotting.java

Ah, this is closer. It calculates the maximal bounds of an animation:
EsotericSoftware/spine-runtimesblob/4.2/spine-ts/spine-player/src/Player.ts#L793-L819

You can get the setup pose dimensions from the CLI:

$ spine -i spineboy-pro.spine
Project info: C:\Dev\spine\spine-launcher\eclipse\user\backup\spineboy-pro-189-0.0.00.spine
  Spine version: 4.0.07
  Dopesheet FPS: 30
  Skeleton: spineboy-pro
    Size: 418.45 x 686.2
...

This size is for the setup pose though, animations can be larger or smaller.