[feature] integrate timezone handling/settings with sockpuppetbrowser/playwright/etc

Since the app already has settings for timezone, it should use the playwright/puppeteer API call to set the timezone in the browser

at `/settings#timedate` it simply needs to read this then set the timezone https://playwright.dev/python/docs/emulation#locale--timezone

https://github.com/dgtlmoon/sockpuppetbrowser/issues/27

https://github.com/dgtlmoon/sockpuppetbrowser/pull/32

sockpuppetbrowser may need the `tzdata` package, but test it anyway

Start with the timezone setting at /settings#timedate, then read the Playwright locale/timezone emulation documentation and the linked sockpuppetbrowser issue and pull request. Verify how the browser integration receives settings and whether tzdata is required. Done means the configured timezone is applied through the browser API and tested with the supported backend.

Written by the indexing model from the issue text.