Learn Turkish: Bu kahve çay gibi. - This coffee is like tea.

In Turkish, the 'to be' verb for the third person ('is') is often just implied. You don't need a separate word for it here. Saying Bu kahve çay gibi perfectly translates to 'This coffee is like tea.'

How does gibi work compared to English?

gibi means 'like' or 'similar to', but because Turkish uses postpositions instead of prepositions, it comes right after the word it applies to. So instead of 'like tea', you say çay gibi (tea like).

How does gibi fit into this lesson about daha (more) and en (most)?

While daha and en are used to compare the degree of something (like being bigger or the biggest), gibi is used to say two things are simply similar. If you wanted to say the coffee is better than tea using this lesson's grammar, you would drop gibi and say Bu kahve çaydan daha iyi (This coffee is better than tea).

Does gibi change its spelling based on vowel harmony like many other endings do?

No, gibi is a separate word, not a suffix that attaches to the end of a noun. Because it stands alone, it does not follow vowel harmony rules with the previous word and always stays exactly as gibi.