Add formatters log option

[KatelynKim]

Description

In a previous ticket, I added the formatters option to the browser pino (related PR). This is in continuation of that ticket to fully replicate the behavior of the formatters option in the non-browser pino in its browser counterpart.

Closes #1904

Testing plan

Create a logger with a log function supplied to the browser.formatters option. Something like:

const logger = pino({
  browser: {
    formatters: {
      log (obj) {
        return {...obj, newField: 'awesome!', level: 'testlevel'}
      }
    }
  }
})

logger.info({ hello: 'world' }, 'Logging')

Ensure the correct log is output. For the example above, it should look something like:

{
  time: 1707885379287,
  level: 'testlevel',
  hello: 'world',
  msg: 'Logging',
  newField: 'awesome!'
}