If you downloaded your .tax2024 file after preparing your return in TurboTax Online, your Chrome OS may save it as a PDF (or only download the PDF), which is of course, good to have!
You may need to email it to yourself, then you may be able to save it in your Drive, or save it to a removable drive.
Remember that your .tax2024 file is saved online, under 'Your Tax Files and Documents', but I understand wanting to have a backup copy of the actual data file. Unfortunately, I couldn't find any info about saving the data file on a Chromebook.
@wcghb