Well, אֶת does not mean the, but is a grammatical particle which indicates that a determined object follows a transitive verb and is therefore only translated by word order in English. Your problem would be similar to saying: Why does the s in he eats mean third person, when there is already the pronoun he".
Well, in the traditional defective orthography you wrote אֹ֫כֶל food without a vav, because it is a segolate of the type KoKK-, where you have forms like אׇכְלִי [okhli] my food written with a Kamatz Katan, so that out of reasons of uniformity of the different forms וֹ was not used in all its forms.
I can't even read my own question it's so full of typos! Thank you for trying to help me; it seems to be over my head, but I'll keep going and maybe it will come to make sense. I looked at a Hebrew verb book too. Apparently it's present tense that has the vav, and also the first person future . I made a list of all the "vav" verbs presented so far: אוהב, אוכל, בוחר, גומר, הולך, זוכר, חושב, חוזר, יודע, יוצא, יורד, יושב, כותב, לובש, לומד, מוכר, מוצא, סוגר, סופר, עובד, עוזב, עומד, עוצר, פוגש, פןתח, רואה, רוצה, רוקד, שואל, שומע, שומר, שותה?
Agreeing with YardenNB's summary...adding a little more. Yod and vav are semi vowels...even in English 'y' can function as a vowel. Hebrew has come a full circle in terms of spelling. Way back in history no vowels were written at all. Then semi vowels started being used as vowels at the ends of words. Then they started being used as vowels in the middle of words. But the only words that were given these vowels were the ones where the vowels never changed. Later on, the niqqud system was perfected and added to the system already in use. So when using niqqud, some vowels are marked twice. Some vowels that could change under certain circumstances were not marked with vav or yod in the old system, but in modern Hebrew, which is generally written without niqqud they are often added to help word recognition. So as Yarden NB says, yods and vavs are used when writing without niqqud, but not when writing with niqqud. But there are some exceptions to this rule. One of these, of course, is the feminine plural ending. Even when written with full niqqud, it stays the same. Another is the word טוב, meaning good. There are some words such as בוקר /גדול which were originally written with or without the vav, so both are equally correct when you are using niqqud. In general, because Duo is not using niqqud, it makes full use of vowel letters. But outside of Duo, expect variations.
I think there is almost zero flexibility in the rules for writing with niqqud (maybe some particular words here and there with two allowed forms), and quite little flexibility without niqqud. Whether all people (and even writers, and even language editors) know the rules well enough to always get it right, or be disturbed by mistakes, is another matter.