Do we need a learning record store to use xAPI?
xAPI is the format and the transport. The learning record store is the place the data lands, and most LMSs do not include one.
What an LRS gives you
Statement-level history, queryable by learner, cohort or activity, and a single store if several systems report into it. Node XR attempt data exports through xAPI into your learning record store, alongside the gradebook.
When you do not need one
If the question is who completed and what they scored, SCORM into the gradebook or a CSV export answers it with nothing extra to buy or run.
One thing to check
If an older recommendation points you at the open-source edition of Learning Locker, note that it has had no release since 2021 and development moved to the commercial product. Confirm what your institution is actually running before planning around it.