I've tracked this issue down to biz.jmaconsulting.grantprograms/CRM/Grant/DAO/Grant.php. That file has significant differences from the DAO that's generated with the latest version of Civi, and has a header that suggests it was initially forked from Civi 4.3. I compared it against the same file from Civi 4.3, and honestly I'm still not sure what the differences are in this file.

For this extension to function, I think it's necessary to pull the DAO/Grant.php from a modern Civi and re-apply the customizations on top of it. For instance, the extension's DAO file doesn't have the getReferenceColumns() function (though adding it doesn't solve the fixes).

An example watchdog issue is here:

| 2983 |   1 | php  | %type: !message in %function (line %line of %file). | a:6:{s:5:"%type";s:5:"Error";s:8:"!message";s:48:"Call to a member function addTableLink() on null";s:9:"%function";s:62:"Civi\Api4\Service\Schema\SchemaMapBuilder->addBackReferences()";s:5:"%file";s:133:"/home/jon/local/groundswell/htdocs/sites/all/civicrm-custom/extensions/org.civicrm.api4/Civi/Api4/Service/Schema/SchemaMapBuilder.php";s:5:"%line";i:143;s:14:"severity_level";i:3;} |        3 |      | http://groundswell.local/civicrm/contact/view?reset=1&cid=480 |         | 127.0.0.1 | 1554309305 |