Intermittent "Required runner group 'x' not found" errors

Describe the bug
We've encountered intermittent "Required runner group 'x' not found" errors during runner assignment in our GitHub Actions workflows.
Runner assignment process observed:

• GitHub actions workflow is triggered
• GitHub scheduler verified runner group exists and sent a request to AWS through GH App webhook
• AWS initialized an ec2 runner and registered in the runner group
• Our ec2 runner took ~2:30min to complete initialization and start processing the job
• Meanwhile, intermittently a job failed in <2min with "Required runner group 'x' not found" error
• In the same workflow matrix, runners got assigned to some jobs successfully and failed for some jobs with the error

We didn't find anything notable in the runner runner/syslogs/user-data logs. Runner remained idle (waiting to pick up a job) until it was terminated, based on worker logs.
we are looking for a direction to investigate..

Job definition:
jobs:
build:
runs-on:
group: x
labels: [ self-hosted, u22-ephem ]
strategy:
fail-fast: false
matrix:
build_matrix: ${{ fromJson(inputs.build_matrix) }}
steps:

Runner group policy:

• allows access to my repository
• Access allowed for all workflows
• Other jobs in the same workflow are able to pick up runners for job compilation

To Reproduce

• Occurs intermittently

Runner Version and Platform

• Runner version - 2.331.0
• OS Platform - Ubuntu 22.04 & 24.04

What's not working?

user-data & Runner's Diagnostic Logs

Start with the provided job definition and compare successful and failed matrix jobs against the runner assignment timeline, runner worker logs, user-data, and diagnostic logs. Done means identifying why the scheduler intermittently reports runner group 'x' as missing despite successful registration, with reproducible evidence or a confirmed cause.