feat: Add page lifecycle hooks to `BrowserPool` #375

Job	Run time
PR title check	4s
Code checks / Spell check	5s
Code checks / Actions lint check	32s
Doc checks / Doc checks / Docs check	1m 50s
Code checks / Lint check / Lint check (3.13)	31s
Code checks / Lint check / Lint check (3.14)	31s
Code checks / Lint check / Lint check (3.11)	26s
Code checks / Lint check / Lint check (3.12)	34s
Code checks / Lint check / Lint check (3.10)	29s
Code checks / Type check / Type check (3.12)	35s
Code checks / Type check / Type check (3.14)	28s
Code checks / Type check / Type check (3.13)	28s
Code checks / Type check / Type check (3.10)	26s
Code checks / Type check / Type check (3.11)	30s
Tests / Unit tests / Unit tests (ubuntu-latest, 3.11)	5m 5s
Tests / Unit tests / Unit tests (ubuntu-latest, 3.10)	4m 51s
Tests / Unit tests / Unit tests (windows-latest, 3.12)	6m 34s
Tests / Unit tests / Unit tests (ubuntu-latest, 3.12)	5m 17s
Tests / Unit tests / Unit tests (windows-latest, 3.10)	6m 49s
Tests / Unit tests / Unit tests (macos-latest, 3.10)	5m 55s
Tests / Unit tests / Unit tests (windows-latest, 3.13)	6m 54s
Tests / Unit tests / Unit tests (macos-latest, 3.11)	3m 44s
Tests / Unit tests / Unit tests (windows-latest, 3.14)	5m 56s
Tests / Unit tests / Unit tests (macos-latest, 3.14)	7m 32s
Tests / Unit tests / Unit tests (ubuntu-latest, 3.13)	4m 46s
Tests / Unit tests / Unit tests (windows-latest, 3.11)	7m 48s
Tests / Unit tests / Unit tests (macos-latest, 3.13)	5m 1s
Tests / Unit tests / Unit tests (ubuntu-latest, 3.14)	3m 51s
Tests / Unit tests / Unit tests (macos-latest, 3.12)	3m 54s
	1h 31m 26s

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