Code clean up to remove starboard/common/atomic usage

[iuriionishchenko]

Code clean up to remove starboard/common/atomic usage

Test-On-Device: true

b/353387554

[kaidokert]

I've reviewed, and changes look correct and good.

However - lets please take this opportunity to also consistently and correctly default-initialize the variables affected by this change.

It seems that the used style is generally std::atomic_var foo{value}; so let's use that everywhere for in-class initialization.

Of course, please doublecheck that the values match the expectation in code as well - in most cases atomic_bool is expected to be default false, but not always.

[kaidokert]

lgtm now - please wait until internal builds come back green and Hao has a chance to review as well.

[iuriionishchenko]

There are 5 failing and 1 errored checks. But I don't have access to full logs to investigate and fix them. Can you provide me?

[kaidokert]

There are 5 failing and 1 errored checks.

With on-device tests those are often flaky failures on the first try. When you see those, please click "Retry" on the failed jobs and see if one retry cleans them up. We don't currently auto-retry yet.

[kaidokert]

Hm there's lint failure from wrong include order - can we get that fixed please as well ?