Implement Lusztig / Geck's construction of semisimple Lie algebras

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Instead of using the Serre relations, one can use a construction of Lusztig / Geck to get the existence part of the semisimple Lie algebra classification.

Details are given in here:
Geck, "On the Construction of semisimple Lie Algebras and Chevalley Groups", Proc. Amer. Math. Soc. 145(8), 2017.

The cost of Geck's approach is that the input to the construction needs to be a root system, rather than a matrix, and the proof of existence thus becomes intertwined with the classification of root systems. The advantage is that there is just much less work overall.

This thus provides an alternate approach to both of: #10071 and #10072

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Some initial PRs in this direction as follows:

• [Merged by Bors] - feat: a finite-dimensional Lie algebra with a irreducible faithful finite-dimensional trace-free representation is semisimple #21614
• [Merged by Bors] - feat: characterise linearly dependent roots of root pairings #21851
• feat: basic structural lemmas about finite crystallographic root pairings. #21932