TC currently shows the parent projects of a user's project memberships in the project list (e.g. https://techcontribs.toolforge.org/uid/chlod#phabricator shows "Cloud Services" and "Tools", whereas @Chlod only shows "Tool-techcontribs"). This isn't ideal since someone in a project might not necessarily have access to its parent projects. It also doesn't have parity with what Phabricator shows on its interface, which is an unspoken goal for TC.
project.search doesn't seem to provide an option for a members constraint where the user is a direct project member, nor does that info seem to be available from the members attachment (it only ever returns an object of type {phid: string}). Scrolling through https://phabricator.wikimedia.org/conduit/, there doesn't seem to be any other API endpoint which allows getting a user's joined groups aside from project.query (which is Frozen), but that doesn't give the proper info either (result.data[*].members is just an array of PHIDs). Based on this, an upstream change might be needed.