I would like to show membership details on the contact summary screen - type, status, start date - using the contact layout editor. I can create a profile for membership, but this isn't available to add, and membership fields can't be added to a block, it seems. As you can have multiple memberships for a contact I can see why it might be tricky. Is it possible to show membership info on the summary screen using the UI?
If you install the Extended Reports extension (available from in-app download), you can place Extended Reports as a block using Contact Layout Editor.
See the screenshot below - I'm using the "Extended Report - Membership Price Set Report" template to generate this report. Under the report's Display Options tab, I clicked Make available for contact summary page.