Here is a response from Google Workspace Support:
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Summary
When using the file picker in Chrome OS, the end user does not see all the folders they expect to see under 'Shared with me' .
The engineering Drive team engaged the Chrome engineering team to confirm the expected behavior reported here and We can confirm this is actually working as intended.
Background
The "Shared with me" right now only returns a certain number of file results due to the performance considerations, the results are returned based on the "last modified" field.
Even if you choose "sort by Name" in the UI, the sorting is based on the already returned result. If you try to align the Drive web to use the same sorting, the result should be consistent.
> In Files app side, sort by "Date modified" in the "Shared with me" UI.
> In Drive web, sort by "Last modified" (without by me).
Please note that the return results limit is imposed by Google to avoid abuse behavior, performance issues and cannot be disclosed.
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And here is my follow-up question:
If this is by design, how then would a user select a file from the Shared with Me section in either the Files app on the Chromebook, or the File Selector window on a Chromebook?
A scenario that was presented to me by one of our users is as follows:
A teacher shares a file with another teacher in September of 2023. In September of 2024, the teacher to whom the file was shared wants to upload that file to a website. However, because the file is only listed in the Shared with Me section, and the Shared with Me section is deliberately selective to which files are available, the file cannot be found or accessed in this manner.