Role dropdown can be inaccurate if you're admin

### Steps to reproduce

1. Enter a room where you're admin, and which contains at least one non-admin
2. Click your own avatar in the timeline, to open the user info panel (other ways to open user info panel may work, I didn't check)
3. Without clicking anything else, click on any non-admin's avatar

### Outcome

#### What did you expect?
Role dropdown should change from "Role in Test: [Admin ↓]" to [Default ↓]

#### What happened instead?
Dropdown does not change, it still reports admin. (If you're not admin, the relevant field is instead plaintext, and it updates correctly.)

This is just a client-side rendering issue, the target user's powerlevel remains where it belongs (except maybe if you interact with the offending dropdown - I didn't try). The dropdown switches to the correct value if the user info panel is closed and reopened, for example by switching to the user list.

I checked the rageshake.tar, and other than some version stuff, it does not seem to contain anything relevant to this issue, just a normal startup and a handful of 'fetching device keys'. It does, however, contain a bunch of room IDs, links posted in the chat (via E Failed to get URL preview [...] /_matrix/media/r0/preview_url?url=https%3A%2F%2F[...] - previews are disabled on my homeserver, per default Synapse config), crypto keys I can't determine if they're private or public, and some other private-looking stuff.

app = element-web
version = 1.9.0
user_agent = Mozilla/5.0 (X11; Ubuntu; Linux x86_64; rv:92.0) Gecko/20100101 Firefox/92.0

### Operating system

Lubuntu 18.04, x86_64

### Browser information

Mozilla/5.0 (X11; Ubuntu; Linux x86_64; rv:92.0) Gecko/20100101 Firefox/92.0

### URL for webapp

app.element.io

### Homeserver

_No response_

### Will you send logs?

No