System tray icon rendered blurry at HiDPI on Windows while a second instance's icon is sharp

### Steps to reproduce

1. Windows 11 with a mixed-DPI multi-monitor setup: a 3840x2160 display alongside a 1920x1200 panel, system scaling 150% (`AppliedDPI` = 144), with different per-monitor DPI offsets.
2. Enable the system tray icon.
3. Start two instances from the same Element Desktop installation: one with the default profile, one with `--profile `.
4. Leave them running across display changes, and compare both tray icons in the notification area.

### Outcome

#### What did you expect?

Both tray icons rendered crisply at the current display scaling.

#### What happened instead?

One instance's tray icon is visibly blurry and upscaled - soft, smeared edges on both the Element logo and the unread badge - while the other instance's icon sits right next to it on the same tray and is sharp.

Observations:

* Both instances run from the same installation and the same version, so differing icon assets can be ruled out.
* The affected instance is the one started with `--profile`, which is also the one that had been running considerably longer (roughly 3 days, against roughly 1 day for the sharp one).

Hypothesis, untested: the tray icon may be rasterised once at the resolution or DPI of the display it is created on at startup, and then not re-rendered when displays are plugged in or out, or when scaling changes during the session. That would fit the longer-running instance being the affected one, and would make the `--profile` flag incidental rather than causal.

### Operating system

Windows 11 Education, 10.0.26200

### Application version

Element Desktop 1.12.26 (x64)

### How did you install the app?

Windows installer from element.io (per-user install under `%LOCALAPPDATA%\element-desktop`)

### Homeserver

_No response_

### Will you send logs?

No

Start by locating the Windows system-tray icon entry point and reproduce the mixed-DPI, multi-monitor scenario with two instances, including one started with --profile. Compare the icons before and after display or scaling changes; done means both tray icons remain crisp at the current display scaling.

Written by the indexing model from the issue text.