Seems we're missing portablization of a file within the Thunderbird Portable profile. Specifically, folderCache.json which looks like it's for recent folders. I've put together a test fix for people to try before the next Thunderbird Portable release. Please give it a try and let me know if it's working as expected for you.
Download ThunderbirdPortable_folderCache_FIX_2023-09-23.zip
SHA256: 7d211a3f2740cd10413e648cd30714efbd75486c773c671c58fd87ed6dce661a
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Download the zip file and replace your existing ThunderbirdPortable.exe launcher with the one included in the ZIP. The GPL source is included in the Other\Source directory as usual.
folderCache.json is for all folders and it gets rebuilt when TB starts if the folders aren't already cached. Dead entries are never cleaned out. It was migrated from Mork to the JSON format here (https://bugzilla.mozilla.org/show_bug.cgi?id=418551) before version 102. Sadly they left the absolute path instead of taking this opportunity to make it profile-relative (see https://bugzilla.mozilla.org/show_bug.cgi?id=1726660).