Performance refactor for Jax BDF Solver, fixes #4455 #10675

Job	Run time
style	23s
Doctests (ubuntu-latest / Python 3.11)	3m 19s
Example notebooks (ubuntu-latest / Python 3.12)	17m 57s
Example scripts (ubuntu-latest / Python 3.12)	14m 2s
Tests (ubuntu-latest / Python 3.9)	29m 50s
Tests (ubuntu-latest / Python 3.10)	30m 4s
Tests (ubuntu-latest / Python 3.11)	26m 36s
Tests (ubuntu-latest / Python 3.12)	34m 2s
Tests (macos-12 / Python 3.9)	27m 42s
Tests (macos-12 / Python 3.10)	28m 34s
Tests (macos-12 / Python 3.11)	29m 36s
Tests (macos-12 / Python 3.12)	28m 27s
Tests (macos-14 / Python 3.9)	11m 32s
Tests (macos-14 / Python 3.10)	11m 48s
Tests (macos-14 / Python 3.11)	19m 5s
Tests (macos-14 / Python 3.12)	8m 59s
Tests (windows-latest / Python 3.9)	30m 52s
Tests (windows-latest / Python 3.10)	32m 47s
Tests (windows-latest / Python 3.11)	28m 19s
Tests (windows-latest / Python 3.12)	28m 54s
	7h 22m 48s

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