Refactor bilinear forms #15907

I just open this to track my progress and let everyone know how I plan to do this. This is very tedious, so if anyone wants to help I would be really happy.

The goal is to completely remove bilin_form R M in favor of M₁ →ₛₗ[σ₁] M₂ →ₛₗ[σ₂] R, which is more general and this removes quite a few boilerplate lemmas since we can apply lemmas from linear_map.
The issue with this refactor is that bilin_form has a few dependencies and moving the lemmas is not trivial (even without the generalization), so doing everything in one PR is not feasible.

The roadmap is as follows:

• [Merged by Bors] - feat(linear_algebra/matrix): Add matrix properties for sesquilinear forms #15906
• Move quadratic form to M₁ →ₛₗ[σ₁] M₂ →ₛₗ[σ₂] R
• Move bilin_form.is_skew_adjoint_bracket to new structure
• Move algebra.trace_form to new structure
• [Merged by Bors] - chore(analysis/inner_product_space/basic): remove bilin_form_of_real_inner #15780
• Remove linear_algebra/matrix/bilinear_form.lean
• Move remaining lemmas from linear_algebra/bilinear_form to linear_algebra/sesquilinear_form and delete linear_algebra/bilinear_form
• (optional/up for debate): rename */sesquilinear_form to*/bilinear_form