I don't want to rain on discovering a genuinely cool bit of theory, but it's not "new" per se.

The equivalence with Einstein summation was noted in this paper [0]. Sandia labs wrote an SQL database based around graphBLAS called TenSQL a few years back. And something similar to your idea of relational algebra as the basis for AI had a paper published earlier this year [1], naming it Tensor Logic.

    Are all of these common operations secretly relational, just with the wrong data model?

Sadly not, but you can get a long way before you find the limits. Modern databases are very well optimized for their use cases, but there's many other possible points in the design space to explore. If you want to really make efficient use of hardware, there are fundamental scaling problems with natural joins because of the combinatorial explosion that gives us WCO though. If you accept an inability to express triangular queries, you can get something that's embarrassingly parallel and scales really flipping well.

If you want to stick to the full relational model, you might be interested in Differential Dataflow [2].

[0] https://arxiv.org/html/2510.12269v3

[1] https://arxiv.org/html/2601.17188v1

[2] https://github.com/TimelyDataflow/differential-dataflow