feat(profiling): Introduce continuous profiling mode - #2830

As per getsentry/rfc#75, this adds the thread data to the spans. This will be
needed for the continuous profiling mode in #2830.

As per getsentry/rfc#75, this adds the thread data to the spans. This will be
needed for the continuous profiling mode in #2830.

The thread data was added to the profile context in #2830. It should live in the
trace context to align with other SDKs.

The thread data was added to the profile context in #2830. It should live in the
trace context to align with other SDKs.

This is a new profiling mode that is mutually exclusive from the existing
profiling modes. In the current profiling modes, a profile is always directly
attached to a transaction. This new mode will continuously emit chunks of
profiling data that will be connected to the span data.

The thread data was added to the profile context in getsentry#2830. It should live in the
trace context to align with other SDKs.

### Description

Removes `ContinuousScheduler.pause()` from
`sentry_sdk/profiler/continuous_profiler.py` (3 lines). It's a stub that
only raises `NotImplementedError`, and nothing implements it or calls
it.

#2830 (Jun 2024, "Introduce continuous profiling mode") added it next to
`ensure_running()` and `teardown()`. Unlike those two, no subclass ever
overrode it, and the SDK never called it. The stub makes it look like
the continuous profiler can be paused, but it can't.

**Evidence**
- `git grep -nw pause` on `master` finds only the definition. Nothing in
`sentry_sdk/`, `tests/`, `scripts/` or `docs/` refers to it.
- `ThreadContinuousScheduler` and `GeventContinuousScheduler`, the only
subclasses, override `ensure_running()` and `teardown()` but not
`pause()`.
- `git log -S "def pause"` finds only #2830. `git log -S ".pause("`
across `sentry_sdk` and `tests` finds no commits, so it has never had a
caller.
- `ContinuousScheduler` isn't exported from `sentry_sdk.profiler`
(`__all__` lists only the transaction-profiler schedulers) and isn't
documented.
- No open PR or issue mentions it. #7275 also touches
`continuous_profiler.py`, but in different hunks
(`ThreadContinuousScheduler.__init__`).

**Why it's safe**
- `ContinuousScheduler` is an internal class. The method is unreachable,
so behavior doesn't change, and no public API or documented behavior is
affected.

**Checks**
- `uv run ruff check` / `ruff format --check` on `sentry_sdk/profiler`:
clean
- `uv run --group typing mypy sentry_sdk`: no issues
- `TESTPATH=tests/profiler uv run tox -e py3.14-common`: 106 passed, 69
skipped. The skipped tests are the gevent cases, which need gevent
installed.

#### Issues
None. Found by the weekly sentry-python removal scout.

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