from a theoretical physicist point of view, i find GA don't add much to the standard tooling ppl use, i.e. Lie algebras, Clifford and (sometimes) differential forms. while it's always nice to have a formalism that "hides indices", in most cases (for (super-)gravitation at least) just writing tensor/clifford/lie indices is just much faster and less error prone.

i used to use differential form for gauge theories, einstein-cartan gravitation and ramond-ramond fields.

also, in a paper, we used O(D,D) clifford algebras/spinors to represent differential forms, which worked quite well in our very specific case (appendix A)

https://arxiv.org/pdf/1304.1472

ps: i had colleagues that worked on GA for ML in robotics but wasn't really impressed by what it accomplished