Get the raw URL of an image in views-view-table.html.twig
Thanks to all, especially @belltouche and @Jaypan, for taking the time to respond. After all the kind suggestions and lots of reading and trial-and-error, I ended up using the following code in views-view-table.html.twig to display an image URL:

{% for i, row in rows %}
  ...
  {% if view.field.field_image.value(view.result[i]) %}
    {{ row.columns.field_image.content|render|striptags|trim }}
  {% endif %}
  ...
{% endfor %}


Note that I'm using the URL to image formatter for the image field in the view.

To explain, view.field.field_image.value(view.result[i]) gets the raw value of the image field, which turns out to be the entity id for the image. Checking it makes a concise test to see if there is an image in the field (if there's a better way, please say so).

It also turns out that there isn't any other information about the image in the raw value. Just the entity id, which is why I could never find the image URL in the raw value.

There was a suggestion made that I could use Twig Tweak to load the image entity by its id and get the URL from it. I'm sure this would have worked, but since my purpose was to avoid the overhead of render|striptags|trim processing, loading the entity after it had already been loaded to produce the content didn't seem an advantage.