Are ellipses always used to indicate omitted text?

Yes; whether it comes at the beginning, middle, or end of a text, an ellipsis indicates that text has been omitted.
No; the ellipses can have many uses and meanings.
Not always, but if an ellipsis comes in the middle of text, it always indicates omitted text.
Not always, but if an ellipsis comes at the end of a text, it always indicates omitted text.

No; the ellipses can have many uses and meanings.

Why might it not be a good idea to use an ellipsis in the second text below?

In order to bake these cookies, you will need butter, flour, baking soda, sugar, and chocolate chips.

In order to bake these cookies, you will need butter…and chocolate chips.
The ellipsis in the second text omits necessary information.
The ellipsis in the second text includes unnecessary information.
The ellipsis in the second text suggests that chocolate chips are the most important ingredient.
The ellipsis in the second text suggests a traditional way of baking.

The ellipsis in the second text omits necessary information.

Not always, but if an ellipsis comes at the end of a text, it typically indicates omitted text. However, it is important to note that ellipses can have other uses and meanings, such as indicating a pause in speech or trailing off in thought.

Not always, but if an ellipsis comes at the end of a text, it often indicates omitted text. However, it's important to note that ellipses can have multiple uses and meanings depending on the context. While they are commonly used to indicate omitted text, they can also be used to show hesitation, trailing off, or a pause in speech, among other things. It's always important to consider the surrounding context to understand the intended meaning of an ellipsis.