Epics behave slightly differently in next-gen projects and this is one example of that. We are formalizing an issue hierarchy in next-gen projects (where we will have parent/child relationships) rather than using epic links. This will facilitate some cool stuff int he future around reporting and roll up estimation. Unfortunately in the short term, it means when you move issues to next-gen projects you will need to manually assign these issues to the relevant epic.
It's important to note the epic link has not actually been removed in the background- it's just not visible and is not useful within the context of the next-gen project. If you were to move your issues back to a classic project, for example, you would not lose this linkage. Although the 'Epic Name' and 'Epic Colour' custom fields would be lost.
In the future, as we build out the next-gen projects, we will provide an automated mechanism to create the new parent/child relationship based on the epic link but it just isn't something we have got to yet. We apologize we didn't make this clear earlier. We have updated our docs in an attempt to clarify how epics behave when migrating projects. You can review the docs from this page.