feat: Add page lifecycle hooks to `BrowserPool` #377

Job	Run time
PR title check	6s
Code checks / Actions lint check	33s
Code checks / Spell check	8s
Doc checks / Doc checks / Docs check	1m 55s
Code checks / Type check / Type check (3.10)	27s
Code checks / Lint check / Lint check (3.10)	30s
Code checks / Lint check / Lint check (3.14)	27s
Code checks / Lint check / Lint check (3.13)	32s
Code checks / Lint check / Lint check (3.11)	31s
Code checks / Type check / Type check (3.12)	31s
Code checks / Type check / Type check (3.11)	26s
Code checks / Type check / Type check (3.13)	26s
Code checks / Type check / Type check (3.14)	34s
Tests / Unit tests / Unit tests (windows-latest, 3.10)	7m 28s
Code checks / Lint check / Lint check (3.12)	26s
Tests / Unit tests / Unit tests (windows-latest, 3.13)	6m 20s
Tests / Unit tests / Unit tests (macos-latest, 3.14)	3m 59s
Tests / Unit tests / Unit tests (macos-latest, 3.11)	5m 2s
Tests / Unit tests / Unit tests (windows-latest, 3.11)	6m 56s
Tests / Unit tests / Unit tests (macos-latest, 3.12)	4m 38s
Tests / Unit tests / Unit tests (windows-latest, 3.14)	5m 12s
Tests / Unit tests / Unit tests (ubuntu-latest, 3.12)	5m 20s
Tests / Unit tests / Unit tests (macos-latest, 3.10)	3m 53s
Tests / Unit tests / Unit tests (macos-latest, 3.13)	3m 42s
Tests / Unit tests / Unit tests (ubuntu-latest, 3.10)	4m 56s
Tests / Unit tests / Unit tests (ubuntu-latest, 3.13)	4m 59s
Tests / Unit tests / Unit tests (ubuntu-latest, 3.14)	3m 45s
Tests / Unit tests / Unit tests (ubuntu-latest, 3.11)	4m 53s
Tests / Unit tests / Unit tests (windows-latest, 3.12)	7m 1s
	1h 25m 36s

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