How can I grant Community Users read access to all accounts and contacts, but only edit access to the logged-in user contact and related account? We have Community User licenses only.
As you are using Customer Community licences you need to use Sharing Sets to allow edit access to their related accounts. Customer Community Plus licences use the standard sharing model unlike high volume licences such as Customer Community.
Sharing Sets can be maintained under Digital Experiences>Settings>Sharing Sets. You can create one or multiple sharing sets and set the permission for the Customer Community profiles to be able to update the Accounts and Contacts related to their user records by granting Read/Write access. See image below