Icons that share the names between packs stay the same

[brawaru]

Describe the bug

When switching between packs, icons that share the names between packs do not update to the one in current pack, causing a mix of icons from multiple packs:

Reproduction

Switch from OpenMoji to Twitter Emoji, then to Noto Emoji

System Info

System:
    OS: Windows 10 10.0.19043
  Browsers:
    Edge: Spartan (44.19041.1266.0), * Chromium (111.0.1661.41)
    Internet Explorer: 11.0.19041.1566

* In use

Used Package Manager

n/a

Validations

• [X] Follow our Code of Conduct
• [X] Read the Contributing Guide.
• [X] Check that there isn't already an issue that reports the same bug to avoid creating a duplicate.
• [X] Check that this is a concrete bug. For Q&A, please open a GitHub Discussion instead.
• [X] The provided reproduction is a minimal reproducible of the bug.