Learn Croatian: Hoćete li probati meso i povrće? - Do you want to try the meat and vegetables?

Because this is a yes/no question that starts with the verb. The short (clitic) forms of htjeti cannot stand at the very beginning of a sentence. When asking a question this way, you must use the full form hoćete followed by the question word li.

Since htjeti is also used to make the future tense, does this mean 'Do you want to try' or 'Will you try'?

It can actually mean both! The verb htjeti plus an infinitive like probati is used both for the present tense of 'wanting' to do something, and to form the future tense. Context usually tells you which one it is. When offering food to guests, treating it as 'Do you want to try' is very natural.

Could I use the verb željeti here instead?

Yes! You could ask Želite li probati.... Both htjeti and željeti can mean 'to want', but željeti (to desire) sounds slightly softer and more polite, similar to 'would you like' in English. Htjeti is a bit more direct.

Why don't the words meso and povrće change their endings, since they are the direct objects being tried?

Because they are both neuter nouns. They are indeed in the accusative case here (the direct object case), but for all neuter nouns in Croatian, the accusative form looks exactly the same as the basic dictionary form.