[PM-38764] Forwarded email aliases are generated immediately upon viewing the page, rather than after confirming

### Steps To Reproduce

1. Go to "Generator"
2. Click "Username"

### Expected Result

Alias should only be generated after clicking a button to confirm.

### Actual Result

Alias will be immediately generated upon viewing the page, which can accidentally generate/save a bunch of unused aliases at the service every time you click generator. It makes it really hard to tell what aliases are real and which are garbage that Bitwarden generated when I didn't need it.

### Screenshots or Videos

_No response_

### Additional Context

The browser extension functions properly, and requires clicking the "generate" button to generate the initial alias, in order to prevent cluttering up the alias service. By default, the alias field simply says `-`.

I am specifically using Addy.io, but I suspect the behavior is the same on any service.

### Build Version

2026.4.2

### What server are you connecting to?

Self-host

### Self-host Server Version

Vaultwarden 1.36.0

### Environment Details

_No response_

### Issue Tracking Info

- [x] I understand that work is tracked outside of Github. A PR will be linked to this issue should one be opened to address it, but Bitwarden doesn't use fields like "assigned", "milestone", or "project" to track progress.

Start at the Android app's Generator screen and follow the Username flow described in the reproduction steps. Reproduce the issue with an Addy.io connection, then trace when the alias is created while the page is viewed versus after confirmation. Done means viewing the page leaves the alias field unset and generation occurs only after the user confirms.

Written by the indexing model from the issue text.