The license and attributions requirements of protomaps/basemaps output depends on the input data.
By default, data sources include:
OpenStreetMap is licensed under the ODbL, a share-alike license which requires attribution. Example:
© OpenStreetMap
OSM-derived water and earth polygons are sourced from osmdata.openstreetmap.de, which is also ODbL licensed. This data is produced by the osmcoastline program written by Jochen Topf and contributors.
Natural Earth is a vector map dataset released to the public domain. The details of its license:
All versions of Natural Earth raster + vector map data found on this
website are in the public domain. You may use the maps in any manner,
including modifying the content and design, electronic dissemination,
and offset printing. The primary authors, Tom Patterson and Nathaniel
Vaughn Kelso, and all other contributors renounce all financial claim
to the maps and invites you to use them for personal, educational, and
commercial purposes.
No permission is needed to use Natural Earth. Crediting the authors is
unnecessary.
More details can be found on the Natural Earth Terms of Use page.