Root Cause

The bounce error in your screenshot:

Delivery has failed to these recipients or groups:
notifications-bot@github.com
The recipient's mailbox is full and can't accept messages now.

happens because your reply was sent to GitHub's automated broadcast address (notifications-bot@github.com) instead of the thread's dedicated reply address.

1. Broadcast Sender vs. Inbound Webhook:
   Addresses like notifications-bot@github.com and notifications@github.com are strictly egress/outbound sender addresses hosted on Microsoft 365 Exchange Online (postmaster@microsoft.com). They have zero inbound storage quota by design and will reject any direct incoming mail with an Exchange NDR (554 5.2.2 mailbox full).
2. How GitHub Ingests Email Replies:
   When GitHub sends a notification for an issue or pull request, it attaches a unique cryptographic Reply-To: header in the format:
   reply+<token>@reply.github.com
   This address does not use an Exchange mailbox; it routes to GitHub's inbound webhook parser, which identifies the repository, pull request, and your user identity to post the comment.

How to Fix

1. Verify the Reply-To Address in Your Mail Client:

   • Open the original notification email and click standard Reply (avoid "Reply to Sender" or "Reply All").
   • Before hitting send, look at the To: field. It must point to reply+...<alphanumeric-hash>...@reply.github.com, not notifications-bot@github.com.
   • If you forwarded the email or used a mail client rule/filter, the Reply-To header may have been dropped or replaced with the sender address. Ensure you reply directly to the original notification message.

2. Verify Your Sender Email Address on GitHub:

   • For security, GitHub matches the From: address of your incoming email against the verified addresses on your account.
   • Go to GitHub Email Settings and confirm that the exact email address you are sending from is listed and marked as Verified. Unverified or mismatched sender addresses are ignored or rejected.

3. Alternative Direct Commenting:
   If your email provider or corporate mail filter strips custom Reply-To headers, you can always post comments directly from the web interface or via the GitHub CLI:

   gh pr comment <pr-number> --repo <owner>/<repo> --body "Your comment here"

If this explains the NDR and gets your email replies working, please consider marking this response as the accepted answer!