This is a known issue reported to our engineering team (CQ-4282307 | Page Move and Rename not working in Touch UI for a large set of content) via internal JIRA IDs CQ-4282943 wherein moving the page in the same folder does not work in touch UI [next button is inactive].
Engineering has fixed the issue in 6.5.4 version already. As a temporarily workaround, you can increase the size property of /libs/wcm/core/content/sites/movepagewizard/destination/field from 40 to 2000, you can try the same on a lower environment & test thoroughly.