closes
[NY-1041](https://linear.app/ghost/issue/NY-1041/oss-issue-welcome-email-sender-still-appears-as-noreply-in-preview)
and #26381

- In #26358 we made it so that
member welcome emails, when sent, would use sender info and reply_to
from the default newsletter
- this PR updates the modal to display that information properly as well
- Since this info is used in both the button that opens the modal and
the modal itself, added a hook to de-duplicate some of the logic for
determining exactly what to display
- No logic yet for updating sender name, email, and reply to
specifically for welcome emails, but this code is written in such a way
that once that's supported it can easily take precedence over default
newsletter values

### State 1 - defaults
The default values for the newsletter (first screenshot) are what
welcome emails use.

<table> <tr> <th>Default Newsletter Settings</th> <th>Welcome Email
Buttons</th> <th>Modal</th> </tr> <tr> <td align="center"><img
src="https://github.com/user-attachments/assets/b41a23a5-0e0b-42a6-b482-9a872c452780"
alt="Screenshot 2026-02-16 at 3 01 30 PM" width="380" /></td> <td
align="center"><img
src="https://github.com/user-attachments/assets/20258e4e-1d4d-4d3d-880c-a91b311b8aa9"
alt="Screenshot 2026-02-16 at 3 02 04 PM" width="380" /></td> <td
align="center"><img
src="https://github.com/user-attachments/assets/63439fd1-7067-47d7-b000-7a22b7bc4f32"
alt="Screenshot 2026-02-16 at 3 01 43 PM" width="620" /></td> </tr>
</table>

### State 2 - custom name and sender email
Updated sender name and sender email for the default newsletter. Sender
name is updated in the button that opens the modal, and name + sender
email are updated in the modal. The test email matches the same values.

<table> <tr> <th>Newsletter Settings</th> <th>Welcome Email Buttons</th>
</tr> <tr> <td align="center"><img
src="https://github.com/user-attachments/assets/5a971b12-3ff0-4195-8a89-a69638b90b75"
alt="Screenshot 2026-02-16 at 3 02 38 PM" width="420" /></td> <td
align="center"><img
src="https://github.com/user-attachments/assets/c5dd8e08-3b53-4f21-8b2e-7955092f50cc"
alt="Screenshot 2026-02-16 at 3 02 48 PM" width="420" /></td> </tr> <tr>
<th>Modal</th> <th>Resulting Test Email</th> </tr> <tr> <td
align="center"><img
src="https://github.com/user-attachments/assets/5eebce17-b11c-40eb-88a7-7edf3a486d0d"
alt="Screenshot 2026-02-16 at 3 02 54 PM" width="420" /></td> <td
align="center"><img
src="https://github.com/user-attachments/assets/20a19864-3a21-4c53-82a0-c521ea7a070e"
alt="Screenshot 2026-02-16 at 3 03 08 PM" width="420" /></td> </tr>
</table>

### State 3 - custom reply to
Same as above, but with a custom reply-to address. It appears in the
modal and in the actual sent email.

<table> <tr> <th>Newsletter Reply-To Setting</th> <th>Modal (w/
Reply-To)</th> <th>Resulting Test Email</th> </tr> <tr> <td
align="center"><img
src="https://github.com/user-attachments/assets/eab3dded-8e52-461c-8665-0565558cf471"
alt="Screenshot 2026-02-16 at 3 03 24 PM" width="380" /></td> <td
align="center"><img
src="https://github.com/user-attachments/assets/c5f1c741-4aac-4648-a82a-cf477c8a5a9e"
alt="Screenshot 2026-02-16 at 3 03 33 PM" width="380" /></td> <td
align="center"><img
src="https://github.com/user-attachments/assets/1633a176-0625-4ebf-b591-1724be037c6a"
alt="Screenshot 2026-02-16 at 3 03 42 PM" width="520" /></td> </tr>
</table>