Unfortunately, your guess is right. Edge is based on Chromium and it's the same for extension APIs. Edge doesn't expose API for Edge Collections so I'm afraid you can't access Collections directly in extension.
Just like you say, we can find Collections data in local file %localappdata%\Microsoft\Edge\User Data\Default\Collections\collectionsSQLite. You can use fetch
in chromium extensions to access local file, but it's an SQLite database. I have the same opinion with you that it can't apply here.
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Regards,
Yu Zhou