How to access image alt value in twig?

Hi @hcanning,
I'm not sure from where you are trying to acess the media image alt value. If you could clarify that it would be great!
I have installed the module and created a paragragraph with a reference field media type image. After that configured the formatter to Thumbnail URL in 'Manage Dispaly' for the paragraph type. Created an entity and referenced the paragraph type. Accessed the media image value using the twig template.
You can try out this, it worked for me.
{{ paragraph.field_test_image.entity.field_media_image[0].alt }}
Here field_test_image - it's the image field name within the paragraph,
field_media_image - it's the default media type image field name.
In case, you still can't access the media alt value in paragraph make sure that you have used media referenced in the paragraph type.
Thanks