Playing civ with "Ancient" ability(like Iconians) allows techs "Precursor Relic Proficiency" + "Precursor Artifact Mastery" which unlock "Precursor Data Matrix" + "Ancient Reliquary" relic starbase modules respectively. Researching these techs however does not allow these starbase modules to be built. From looking at StarbaseModuleDefs.xml in the game files, it appears these modules have a dependency on the starbase "Nanite Decryption Center" module - which also cannot be built. I believe this is due to it listing

<Option>Tech_PrecursorArtifactStudies</Option>

as a prerequisite - with no such tech being available in MasterTechDefs.xml. There is a "Tech_ArtifactStudies" listing - with its description being "Precursor Artifact Studies" which potentially was the intended prerequisite. Replacing above option with

<Option>Tech_ArtifactStudies</Option>

and starting a new game allows the "Nanite Decryption Center" module to be built - which subsequently unlocks the "Precursor Data Matrix" and "Ancient Reliquary" modules assuming techs are researched.