`--log-level` flag doesn't behave as [originally/incorrectly] assumed on `ha core logs`

## Describe the problem

When running a command such as:

```
ha core logs --log-level=ERROR
ha supervisor logs --log-level=WARNING
```

the flag is silently ignored, all log entries are returned regardless of severity.

**Example Command and Response**
```
ha supervisor logs --log-level=ERROR
2026-05-19 09:27:44.620 INFO (MainThread) [supervisor.api.middleware.security] /core/info access from a0d7b954_ssh
2026-05-19 09:28:02.494 INFO (MainThread) [supervisor.api.middleware.security] /core/logs access from a0d7b954_ssh
2026-05-19 09:28:54.568 INFO (MainThread) [supervisor.api.middleware.security] /supervisor/logs access from a0d7b954_ssh
```

## Debug information

1. SSH App type

- [ ] Community
- [ ] Core
- [ ] Custom

2. Version of the CLI

```
ha cli info
update_available: false
version: 2026.05.0
version_latest: 2026.05.0
```

3. Version of Home Assistant Core & the Home Assistant Supervisor

Home Assistant Core: `2026.5.1`
Home Assistant Supervisor: `2026.05.0`

4. Output from executing the command with debug info

e.g., `ha hardware info` should be run as `ha --log-level debug hardware info`
```txt

```
_Provided above_

On review of the suggested command above, I'm questoning whether `--log-level` is as I originally assumed it was to be used. The above leads me to believe its the log level of the CLI itself, rather than the output for `ha core|supervisor logs`

## Expected behavior

As stated above, my assumption was that `log-level` would control the output of logs returened on `ha .. logs`. On review of the flag being a Global Flag, I believe my assumption was incorrect.

Rather than a bug (if indeed it's not a bug), would the maintainers be open to a new flag as a feature (or re-using the existing flag in some form)? I'm open to driving any enhancement myself.

The alternative to this enhacement would be that the consumer of the logs (client-side) is responsible for filtering as part of any scripting/log consumption.

My use-case is that I wish to on a daily basis, fetch only errors or warnings from the previous 24 hours. By using a log-level flag, I could return a much smaller subset of logs to be parsed. Similarly, to help in this endeavour, new flags such as `--from DATETIME` and `--to DATETIME` would also greatly help. [I realise this bug report has now become a feature request 😄 ]

Start with the command handling for `ha core logs` and `ha supervisor logs`, then compare it with the global `--log-level` behavior shown by `ha --log-level debug hardware info`. Determine how log severity filtering should apply to returned entries and whether time bounds are part of the feature; done means the requested filters work without changing the global CLI logging semantics.

Written by the indexing model from the issue text.