I have a website that was built and hosted by a web development firm. I have about 50 blog posts with about 50 (Adobe standard license) images licensed under the developer's Adobe Stock account. Copyright to the overall site is mine. I am now moving the site and hosting on my own. The developer is saying that I have to delete all images, which doesn't make sense since I'm not changing the content and simply moving it to a different web host; the content of the blog posts featuring the images is unchanged. Does anyone have insight into this?
This is a question that none, without insight into your contracts, can tell you.
However, if the website is yours, the blog entries are yours and the licences are yours (i.e. the images got licensed for you) then you should be good, except if the contract you had with that company is saying something different.
If I were the company, you could move the blog posts with the assets, as you would be the attributed sublicensee anyhow.
Look here for more information on licensing: https://community.adobe.com/t5/stock/links-for-licensing-terms/td-p/11366788
(Disclaimer: As always with licensing, this is my interpretation of the rules. I think they are correct and advice is based on reading and interpreting the licence terms and on fair use for both the buyer and the artist/stock company, but I cannot rule out that my interpretation is wrong. I'm not an Adobe employee).