test: Add more integration tests #678

Job	Run time
Code checks / Actions lint check	34s
Docstrings checks / Docstrings checks	11s
Package check / Package check	20s
Code checks / Spell check	6s
PR title check	3s
Tests / Integration tests (3.14, ubuntu-latest)	2m 49s
Doc checks / Doc checks / Docs check	1m 16s
Code checks / Type check / Type check (3.14)	10s
Code checks / Lint check / Lint check (3.11)	10s
Code checks / Lint check / Lint check (3.14)	20s
Code checks / Lint check / Lint check (3.13)	11s
Code checks / Type check / Type check (3.12)	13s
Tests / Integration tests (3.11, ubuntu-latest)	2m 52s
Tests / Unit tests / Unit tests (windows-latest, 3.12)	1m 18s
Tests / Unit tests / Unit tests (windows-latest, 3.11)	1m 18s
Tests / Unit tests / Unit tests (ubuntu-latest, 3.11)	47s
Code checks / Type check / Type check (3.11)	12s
Code checks / Lint check / Lint check (3.12)	11s
Tests / Unit tests / Unit tests (windows-latest, 3.13)	1m 10s
Tests / Unit tests / Unit tests (ubuntu-latest, 3.13)	54s
Tests / Unit tests / Unit tests (ubuntu-latest, 3.12)	44s
Tests / Unit tests / Unit tests (windows-latest, 3.14)	1m 47s
Tests / Unit tests / Unit tests (ubuntu-latest, 3.14)	42s
Code checks / Type check / Type check (3.13)	10s
	18m 28s

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