chore: Send Booleans as `true` or `false` to API #330

Job	Run time
PR title check	5s
Tests / Integration tests (3.14, ubuntu-latest)	2m 11s
Tests / Integration tests (3.11, ubuntu-latest)	2m 9s
Code checks / Spell check	5s
Docstrings checks / Docstrings checks	19s
Doc checks / Doc checks / Docs check	1m 21s
Code checks / Actions lint check	31s
Code checks / Type check / Type check (3.11)	10s
Code checks / Type check / Type check (3.13)	12s
Code checks / Lint check / Lint check (3.13)	14s
Code checks / Type check / Type check (3.12)	13s
Code checks / Lint check / Lint check (3.11)	12s
Tests / Unit tests / Unit tests (ubuntu-latest, 3.12)	55s
Tests / Unit tests / Unit tests (ubuntu-latest, 3.14)	51s
Code checks / Type check / Type check (3.14)	13s
Tests / Unit tests / Unit tests (windows-latest, 3.14)	1m 15s
Tests / Unit tests / Unit tests (windows-latest, 3.11)	1m 12s
Tests / Unit tests / Unit tests (ubuntu-latest, 3.11)	57s
Code checks / Lint check / Lint check (3.14)	10s
Code checks / Lint check / Lint check (3.12)	10s
Tests / Unit tests / Unit tests (ubuntu-latest, 3.13)	55s
Tests / Unit tests / Unit tests (windows-latest, 3.13)	1m 12s
Tests / Unit tests / Unit tests (windows-latest, 3.12)	1m 17s
	16m 49s

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