How do I migrate blog post images from one domain to a new one?

The conflicting articles I am finding on the web are leaving me more confused… 🙂

For backstory, I work for a company that has been acquired by another. I am now tasked with moving all the blog post from our old website to a new one. I understand the “Export” tool will export the posts themselves, but to my understanding/reading, it will not include the image files themselves, only the file path (or am I misunderstanding?).

Is my only solution to manually upload my entire media library via SFTP? My media library is quite large, about 2,500 images. I would love an automated process.

Thank you in advance!