Update to Playwright 1.44

[tmbrbr]

Version bump:

• Playwright 1.44: https://github.com/microsoft/playwright/tree/release-1.44
• Firefox v123: f8704c84a751716bad093b9bdc482db53fe5b3ea

Skipping playwright patches for 1.43 as there was no browser patch change since 1.42.

[cla-assistant[bot]]

Thank you for your submission! We really appreciate it. Like many open source projects, we ask that you all sign our Contributor License Agreement before we can accept your contribution.
1 out of 18 committers have signed the CLA.

:white_check_mark: tmbrbr
:x: Ed
:x: eemeli
:x: emilio
:x: jrmuizel
:x: allstarschh
:x: jandem
:x: nchevobbe
:x: wisniewskit
:x: padenot
:x: bgrins
:x: Mossop
:x: jcsteh
:x: valenting
:x: PrototypeNM1
:x: skhamis
:x: eeejay
:x: mfromanmoz

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