feat(browser): support nestedKey in asObject mode and browser.write

[lx3133584]

Problem

When using pino in browser / isomorphic environments with browser.asObject: true (or custom browser.write), the nestedKey configuration option was ignored. Logged payload objects were assigned directly to the top-level log object rather than nested under nestedKey, creating an inconsistency between Node.js and browser runtimes.

Root Cause

• setOpts in browser.js did not store nestedKey.
• asLogObject unconditionally called Object.assign(logObject, argsCloned.shift()) for all object arguments instead of nesting payload objects under logObject[opts.nestedKey] while keeping bindings at the top level.

Fix

• Stored nestedKey: opts.nestedKey || opts.browser.nestedKey || null in setOpts.
• Updated asLogObject to assign payload objects (lvl === 0) to logObject[opts.nestedKey] while assigning binding objects (lvl > 0) to the top-level logObject.

Testing

• Added unit tests in test/browser.test.js verifying that nestedKey nests payload objects under the configured key in root and child loggers.
• Verified all 198 browser tests and lint pass cleanly.

[kilisamemarisaaa]

I found one correctness issue in the collision path. I reproduced it against this head with Node 24.12.0 and compared the emitted objects with the regular Node logger behavior; details are inline.

[kilisamemarisaaa]

This reuses a same-named child binding as the payload container. On this head, child({ payload: 'binding' }).info({ foo: 'bar' }, 'hello') emits {"payload":"binding","msg":"hello"} in browser asObject mode, so the logged object is lost; the Node logger emits payload: { foo: "bar" }.

If the binding is an object, Object.assign mutates that shared binding instead: two successive logs with { first: 1 } and { second: 2 } make both already-collected records end up with payload: { binding: true, first: 1, second: 2 }.

Please create a fresh nested payload object for each log (overriding a colliding binding) rather than using ||, and add regression cases for primitive/object collisions plus two consecutive log calls.