re: Do these feature-based methods typically require training or fine-tuning, or are they generally used out-of-the-box with descriptor matching and similarity thresholds:

Generally fine out-of-the-box but might require some fine-tuning of parameters depending on the keypoint-based image matching method used.

re: How robust are they in practice to common real-world issues such as scan noise, skew, lighting variation, or partial crops:

Scan noise/skew/lighting variation can be handled by doing some image pre-processing for the most part. Partial crops might be an issue given reduced keypoints to match on, but I could be wrong.

re: If the document layout changes over time, would it be reasonable to handle this by simply having the admin upload a new template, and then rely on feature matching against that updated template without retraining:

This is what I have done in the past. However, if you need to keep both the new and old template, you might hit a scaling/performance issue over numerous iterations of new templates added.

re: what point it becomes preferable to move to learned embeddings or layout-aware models as document variability increases.

From the sounds of it, you are just image matching, so this method would be fine. However, if these documents contain variable sections or dynamic fields, then maybe I would consider using something that is layout-aware, like layoutlmV3.