Lethal Tempo and Conqueror are the most consistent rune pages for Azir. You typically run these runes against Bruisers, tanks, and short ranged champions and play off of your auto-attacks. Lethal Tempo is the better one of the two. The buff you get from Lethal Tempo is just more valuable than what you get from Conqueror. Conqueror is a good alternate if you feel like you need more sustain more than attack speed. Swap Gathering Storm for Manaflow Band if you struggle with Mana.

I usually go First Strike if I'm against a short ranged champion or champions who are more squishy. Good late-game scaling. Swap Gathering Storm for Manaflow Band if you struggle with Mana. Or swap Future's Market for Biscuit Delivery.

Run Arcane Comet against long-ranged matchups and trade pokes. Also good against short-ranged Assassins. Change Cheap Shot for Taste of Blood for sustain. Ingenious Hunter for Ultimate Hunter if you aren't going Luden's Tempest.

Your general Mythic Item is Luden's Tempest. Also when against squishy champions.

Buy Liandry's Anguish when you are going against frontline Bruiser/Tank champions. And a melee-heavy or HP stacking team.

Buy Crown of the Shattered Queen if you are against burst champions who can all-in dive you.

Your build path is quite literally the same every single time.

I almost always go Nashor's Tooth over Shadowflame every game, unless I need more Magic Pen. But Void Staff should be enough already anyways. though Nashor's Tooth passive is useless with your soldiers, the 100 AP and 50 ATK SPEED is very valuable. It allows you to take towers faster.

For the situational items, buy Morellonomicon if the enemy has a lot of healing. Banshee's Veil against CC or heavy AP. Rylai's Crystal Scepter against heavy Melee team-comp. And Mejai's Soulstealer if you are super fed. You will swap your other defensive items for your situational items. Or Nashor's Tooth if you need the other defensive items.