remote: Polish for connection progress & error dialogs (#19379)

Before/after:

![err1-before](https://github.com/user-attachments/assets/43d959b3-c9d9-45dd-938e-42d34ec1cfc5)

![err1-after](https://github.com/user-attachments/assets/311d53e0-752c-4eb8-9816-64b1970c228d)

Before/after (I feel like text-wrapping would be more useful than
text-ellipsis here, but I don't see any wrap function):

![err2-before](https://github.com/user-attachments/assets/1626cda9-bf06-43fe-9b7d-3ec64f4db08a)

![err2-after](https://github.com/user-attachments/assets/749a6950-1409-4e75-808e-a1a96dbfc87e)

Before/after:

![prog-before](https://github.com/user-attachments/assets/f5f5a171-db42-4797-bab0-ad71c750bb20)

![prog-after](https://github.com/user-attachments/assets/b52a7694-36f6-4f7a-8a90-ceb223f12ec1)

Release Notes:

- N/A