chore: Send Booleans as `true` or `false` to API #345

Job	Run time
PR title check	5s
Tests / Integration tests (3.11, ubuntu-latest)	2m 10s
Tests / Integration tests (3.14, ubuntu-latest)	2m 20s
Doc checks / Doc checks / Docs check	1m 15s
Code checks / Actions lint check	34s
Code checks / Spell check	4s
Docstrings checks / Docstrings checks	11s
Code checks / Lint check / Lint check (3.12)	13s
Tests / Unit tests / Unit tests (ubuntu-latest, 3.11)	36s
Code checks / Type check / Type check (3.12)	10s
Tests / Unit tests / Unit tests (ubuntu-latest, 3.12)	42s
Code checks / Type check / Type check (3.13)	9s
Code checks / Lint check / Lint check (3.13)	12s
Tests / Unit tests / Unit tests (windows-latest, 3.13)	53s
Tests / Unit tests / Unit tests (windows-latest, 3.11)	3m 25s
Tests / Unit tests / Unit tests (windows-latest, 3.12)	1m 12s
Code checks / Type check / Type check (3.11)	11s
Tests / Unit tests / Unit tests (ubuntu-latest, 3.13)	39s
Code checks / Lint check / Lint check (3.11)	18s
Code checks / Type check / Type check (3.14)	11s
Tests / Unit tests / Unit tests (windows-latest, 3.14)	1m 44s
Code checks / Lint check / Lint check (3.14)	11s
Tests / Unit tests / Unit tests (ubuntu-latest, 3.14)	43s
	18m 8s

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