ENH: rework tree serialization, accompanying tests #26

Job	Run time
standard / Documentation / Python 3.9: documentation building	39s
standard / pre-commit checks / pre-commit	15s
standard / Conda (3.11, true) / Python 3.11: conda	1m 21s
standard / Conda (3.10) / Python 3.10: conda	1m 26s
standard / Conda (3.12, true) / Python 3.12: conda	1m 20s
standard / Conda (3.9, true) / Python 3.9: conda	1m 33s
standard / Pip (3.10) / Python 3.10: pip	1m 9s
standard / Pip (3.11, true) / Python 3.11: pip	1m 1s
standard / Pip (3.12, true) / Python 3.12: pip	1m 8s
standard / Pip (3.9, true) / Python 3.9: pip	1m 6s
standard / Documentation / Documentation deployment	0s
	10m 58s

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