Issue confirmed, thanks for Report.

After patching a bit /administrator/components/com_categories/tmpl/categories/default_batch_body.php

I can get here:

default_batch_body.php.zip

In fact some styling is also broken elsewhere (batch menu items and also batch articles, but not as bad),
That can be solved a bit as shown above (as back-end template is WIP, I wonder if it is worht it), but remains the fact that if choosing a category or menu item (for all batches) the "Do you want to move the items or make a copy of them? " is always displayed while it should only display for example when a category has been chosen.

See 3.8.x to see the correct behavior.
Ir goes from style="display: none;" to style="display: block;"

@dgrammatiko
Display or not of the batch-copy-move id depends on
/build/media_src/layouts/joomla/html/batch/batch-WHATEVER.es6.js

(test here with Firefox)

Can you do something?

We can also use the API and use in the default_batch_body.php this shorther code

		<?php if ($published >= 0) : ?>
			<div class="form-group col-md-6">
				<div class="controls">
					<?php echo JLayoutHelper::render('joomla.html.batch.item', array('extension' => $extension)); ?>
				</div>
			</div>
		<?php endif; ?>

But we still have the issue with js.

@infograf768 it's a simple fix I'll do a PR later on

Please test #21697

Closing as we have a patch

I should say, Thank you to everyone involved.