Starting the phone with Volume down gets you into fastboot mode, not TWRP recovery.
To get into recovery, start the phone with Volume up .
TWRP does not do a complete backup, it even gives a message about that when doing backups. With TWRP you get a complete backup of the system (the OS), but because of the complicated nature of Android internal storage (something along those lines, layman here) it doesn’t handle data stored there (pictures, calendar, contacts, music, ringtones and whatnot …).
For the data, you have to take additional measures, often recommended for this are Titanium Backup on the phone or MyPhoneExplorer for Windows PCs, but you could have a look at these threads …
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