Bitwarden's Firefox Extension breaks keyboard inputs after first use

### Steps To Reproduce

Currently on Bitwarden's v1.53.0 Firefox extension.

1. Click on the Bitwarden Firefox extension, to copy a username/password/any information
2. Paste into a field of your choice
3. Observe that the extension is currently in "selected" mode, even after moving the focus away from it (as shown in attached image)
4. Firefox keyboard functionality is now broken, like using the arrow keys to move the cursor back and forth, block text select like Ctrl + \, etc.


### Expected Result

1. The extension should not be in "selected" mode, once the focus has shifted away from it
2. Keyboard functionality should not be affected

### Actual Result

Described in "Steps to reproduce"

### Screenshots or Videos

_No response_

### Additional Context

Have the following Firefox extensions installed

1. Bitwarden
2. Decentraleyes
3. Disable WebRTC
4. DuckDuckGo privacy essentials
5. Facebook Container
6. Firefox Multi-account containers
7. Firefox Relay
8. HTTPS Everywhere
9. Privacy Badger
10. React Developer Tools
11. Reddit Enhancement Suite
12. Refined Github
13. uBlock Origin
14. Unofficial Netflix Party Plugin
15. User-Agent Switcher and Manager
16. Vimium
17. Zoom Redirector

I have tried re-installing the extension, to no avail.

### Operating System

Linux

### Operating System Version

On Solus 4.3 Budgie DE, with Linux Kernel v5.14.12

### Web Browser

Firefox

### Browser Version

93.0

### Build Version

1.53.0

Start by reproducing the keyboard-input failure in the Bitwarden Firefox extension v1.53.0 on Firefox 93, following the listed steps. Trace the extension's selected-mode and focus handling; done means moving focus away clears that mode and Firefox arrow-key and text-selection behavior remains functional.

Written by the indexing model from the issue text.