Learn Turkish: Mangal yapamayacağız, bari fırında pizza pişirelim. - We won't be able to have a barbecue, we might as well bake pizza in the oven.

Bari adds a feeling of resignation. It shows that baking pizza is a minimum acceptable alternative. It conveys the idea of 'since we can't do our ideal plan (the barbecue), we might as well settle for this instead.'

Could I replace bari with en azından or hiç olmazsa in this sentence?

Yes, you can use either en azından or hiç olmazsa here without changing the core meaning. They all express 'at least.' However, bari is especially natural here because it strongly pairs with making a backup suggestion out of mild disappointment, matching the 'we might as well' translation perfectly.

Why is there an extra -a- before the negative -ma- in yapamayacağız?

That -a- is the impossibility marker. While yapmayacağız means the simple negative 'we won't do it' (by choice), yapamayacağız means 'we won't be able to do it' (due to bad weather, lack of time, etc.). This lack of ability is exactly what forces the speaker to use bari for a backup plan.

Why does the sentence switch from the future tense in yapamayacağız to the -elim ending in pişirelim?