Break up app.rs into parts (#2303)

### What
Part of:
* #2242

Breaks up `app.rs` into several files. This required adding `pub(crate)`
on some fields. I plan to remove that in a future PR, creating accessors
and helpers instead.

This PR doesn't change behavior; it just moves code around.

### Checklist
* [x] I have read and agree to [Contributor
Guide](https://github.com/rerun-io/rerun/blob/main/CONTRIBUTING.md) and
the [Code of
Conduct](https://github.com/rerun-io/rerun/blob/main/CODE_OF_CONDUCT.md)

<!-- This line will get updated when the PR build summary job finishes.
-->
PR Build Summary: https://build.rerun.io/pr/2303

<!-- pr-link-docs:start -->
Docs preview: https://rerun.io/preview/3ef7f88/docs
<!-- pr-link-docs:end -->

crates/re_data_ui/src/image.rs

@@ -26,7 +26,8 @@ impl EntityDataUi for Tensor {
     ) {
         re_tracing::profile_function!();
 
-        match ctx.cache.entry::<TensorDecodeCache>().entry(self.clone()) {
+        let decoded = ctx.cache.entry::<TensorDecodeCache>().entry(self.clone());
+        match decoded {
             Ok(decoded) => {
                 let annotations = crate::annotations(ctx, query, entity_path);
                 tensor_ui(

crates/re_space_view_spatial/src/scene/parts/images.rs

@@ -61,13 +61,13 @@ fn to_textured_rect(
     let Some([height, width, _]) = tensor.image_height_width_channels() else { return None; };
 
     let debug_name = ent_path.to_string();
-    let tensor_stats = ctx.cache.entry::<TensorStatsCache>().entry(tensor);
+    let tensor_stats = *ctx.cache.entry::<TensorStatsCache>().entry(tensor);
 
     match gpu_bridge::tensor_to_gpu(
         ctx.render_ctx,
         &debug_name,
         tensor,
-        tensor_stats,
+        &tensor_stats,
         &ent_context.annotations,
     ) {
         Ok(colormapped_texture) => {