[Ports]: Backport client side changes for 1.53

[microsoft-playwright-automation[bot]]

Please backport client side changes:

• [ ] https://github.com/microsoft/playwright/pull/35645
• [ ] https://github.com/microsoft/playwright/pull/35686
• [ ] https://github.com/microsoft/playwright/pull/35721
• [ ] https://github.com/microsoft/playwright/pull/35722
• [ ] https://github.com/microsoft/playwright/pull/35723
• [ ] https://github.com/microsoft/playwright/pull/35800
• [ ] https://github.com/microsoft/playwright/pull/35809
• [ ] https://github.com/microsoft/playwright/pull/35852
• [ ] https://github.com/microsoft/playwright/pull/35888
• [ ] https://github.com/microsoft/playwright/pull/35759
• [ ] https://github.com/microsoft/playwright/pull/35902
• [ ] https://github.com/microsoft/playwright/pull/35911
• [ ] https://github.com/microsoft/playwright/pull/35917
• [ ] https://github.com/microsoft/playwright/pull/35903
• [ ] https://github.com/microsoft/playwright/pull/35851
• [ ] https://github.com/microsoft/playwright/pull/35926
• [ ] https://github.com/microsoft/playwright/pull/35947
• [ ] https://github.com/microsoft/playwright/pull/35978
• [ ] https://github.com/microsoft/playwright/pull/35969
• [ ] https://github.com/microsoft/playwright/pull/35979
• [ ] https://github.com/microsoft/playwright/pull/35994
• [ ] https://github.com/microsoft/playwright/pull/35988
• [ ] https://github.com/microsoft/playwright/pull/36017
• [ ] https://github.com/microsoft/playwright/pull/36019
• [ ] https://github.com/microsoft/playwright/pull/36030
• [ ] https://github.com/microsoft/playwright/pull/36037
• [ ] https://github.com/microsoft/playwright/pull/36025
• [ ] https://github.com/microsoft/playwright/pull/36046
• [ ] https://github.com/microsoft/playwright/pull/36055
• [ ] https://github.com/microsoft/playwright/pull/36058
• [ ] https://github.com/microsoft/playwright/pull/36054
• [ ] https://github.com/microsoft/playwright/pull/36081
• [ ] https://github.com/microsoft/playwright/pull/36104
• [ ] https://github.com/microsoft/playwright/pull/36079
• [ ] https://github.com/microsoft/playwright/pull/36119
• [ ] https://github.com/microsoft/playwright/pull/36091
• [ ] https://github.com/microsoft/playwright/pull/36154
• [ ] https://github.com/microsoft/playwright/pull/36178
• [ ] https://github.com/microsoft/playwright/pull/36196