IDE2 cannot recover 3rd party package index if the `package_${3RD_PARTY_PACKAGE_NAME}_index.json` is deleted between sessions

Describe the problem

When the package index of a 3rd party platform is removed from the directories.data folder AND neither the primary package index nor the library index is "corrupted". IDE2 cannot recover the 3rd party package. Hence the 3rd party package is not visible from the Boards Manager widget.

To reproduce

⚠️ Be careful. You might corrupt your data folder if you do not know what you are doing.

Rename or delete directories.data,
Make sure you have https://www.pjrc.com/teensy/package_teensy_index.json set as board_manager#additional_urls,
Start IDE2. The CLI can recover. Open the Boards Manager and search for teensy and verify that you see the 3rd party core.
Stop IDE2 and delete directories.data/package_teensy_index.json,
Start IDE2, open the Boards Manager and search for teensy; it's missing.

IDE2 only recovers when there is a primary package index, library index, or platform tools problem, but not with a 3rd party index problem.

Expected behavior

IDE2 can recover missing 3rd party platforms on startup

Arduino IDE version

2.0.4

Operating system

macOS

Operating system version

12.6.3

Additional context

The periodic (every 4 hours) index update should fix the issue.
Or one can run the index update manually. I see some glitches, though. The Boards Manager does not immediately show the recovered core.

https://user-images.githubusercontent.com/1405703/233071157-65c369ae-f648-4288-87ae-19e10830ac2a.mp4

Issue checklist

[X] I searched for previous reports in the issue tracker
[X] I verified the problem still occurs when using the latest nightly build
[X] My report contains all necessary details

arduino / arduino-ide