[Request] Continuous installation option when using legacy installer

### Guidelines

- [x] I have searched the issue tracker for [open](https://github.com/Droid-ify/client/issues) and [closed](https://github.com/Droid-ify/client/issues?q=is%3Aissue+is%3Aclosed) issues that are similar to the feature request I want to file, without success.
- [x] I'm not requesting app support for a specific repo — that's up to repo maintainers
- [x] I understand this might not get built (Droid-ify is maintained by a single person)

### Problem

I activated dhizuku and InstallerX to have a good installing experience without double-checking (well, shizuku dies when I reboot on my device), but it was stopped when I'm performing bulk update, since droid-ify won't request installation automatically using legacy installer, and I have to click those notifications to ask droid-ify to do that.

### Proposed solution

Add a continuous installation switch, which makes driod-ify requests installation automatically when it's using legacy installer, like what it does using shizuku or root.

### Extras

_No response_

Start by tracing the legacy installer path and the bulk-update notification handling in the Android client. Identify where installation requests are gated, then verify that a continuous-installation switch automatically requests each legacy installation without requiring notification clicks.

Written by the indexing model from the issue text.