[rush] rush alert should honor `-q` and `--json` and similar

[stijnveenman]

Summary

When rush alerts is used, utilities that rely on output could fail if the alert is triggered. shouldRestrictConsoleOutput should probably be honored on rush alerts.

Repro steps

run any command that relies on output, like rush list --json | jq

Expected result:
Only JSON should be written to STDOUT

Actual result:
Rush alerts are written to stdout, resulting in an error

jq: parse error: Invalid numeric literal at line 4015, column 0

Details

Standard questions

Please answer these questions to help us investigate your issue more quickly:

Question	Answer
@microsoft/rush globally installed version?	5.153.1
rushVersion from rush.json?	5.153.1
useWorkspaces from rush.json?	undefined
Operating system?	Mac / Linux
Would you consider contributing a PR?	No
Node.js version (node -v)?	22.14.0

[iclanton]

Looks like this was an oversight when that feature was implemented. Should be a fairly easy fix.