[Bug] Incorrectly subtitled program

[nanotyrannus]

Version

firefox:
  Installed: 1:130.0~1725383622~22.04~e64e90b
  Candidate: 1:130.0~1725383622~22.04~e64e90b
  Version table:
 *** 1:130.0~1725383622~22.04~e64e90b 1001
       1001 http://apt.pop-os.org/release jammy/main amd64 Packages
        100 /var/lib/dpkg/status
     1:1snap1-0ubuntu2 500
        500 http://apt.pop-os.org/ubuntu jammy/main amd64 Packages

Description

I have two Firefox installations, one from a repo and one from Flatpak. When no program is open, the launcher correctly detects both, subtitling one as "System" and the other as "Flatpak". However, when I have the "System" Firefox running, the launcher and alt+tab dialog says "Flatpak".

Steps to reproduce

1. Install Firefox via apt
2. Install Firefox via flatpak
3. Open Firefox labeled "System"
4. Open launcher