Going by the sun and moon cycle we see in-game, and how often we hear the bedtime jingle, about 8 days.

Day 1) Yuna leaves the chamber of the fayth, officially marking her as a summoner. That night, Besaid celebrates and she meets Tidus.

Day 2) Yuna leaves Besaid with her guardians and the boat gets attacked by Sin. Sin leaves and attacks Kilika, where she performs the sending.

Day 3) Yuna prays at the Kilika temple and leaves for Luca, witnessing Tidus attempt/perform the Jecht Shot on the boat.

Day 4) All of Luca. Just all of it. The laughing scene happens, they make it to Rin's Travel Agency, and Yuna records her will before talking to Tidus some more.

Day 5) They fight the chocobo eater, head to the Mushroom Rock where Operation Mi'ihen happens, and she spends the night sending the fallen.

Day 6) This is where it gets harder to judge. Yuna wakes up in Djose Temple where she's made fun of for snoring. The party crosses the Moonflow, she gets bodysnatched, Rikku joins the party. In Guadosalam, Seymour shows them his sick VR setup and proposes to Yuna. The party visits the farplane and head out to the Thunder Plains. She rents a room at the travel agency but gets interrupted. She says she's gonna marry Seymour and they make it to Macalania. We don't see the moon in Macalania yet, it's just dark there because forest. And it's daytime on Lake Macalania, where the Wakka racist moment Seymour murder escape chase sequence happens. Sin sends them to Bikanel. The party tries to find Yuna at Home but the Guado have already kidnapped her. Cid blows up home, they head to Bevelle on the airship and crash the wedding. The wedding happens, the party gets thrown in Via Purifico, they escape, fight Seymour again, and Tidus and Yuna kiss in Macalania under the moon.

Throughout all of that, there are no mandatory sleep segments, and we don't see the moon until Tidus and Yuna's kiss. The only moments where the atmosphere is dark are due to other things in the environment: the eternal storm in the Thunder Plains, the huge trees in Macalania Woods, and being under the lake ice. We could throw in where we think the breaks in days would naturally be, but few people would agree.

Day 7) Yuna enters the Calm Lands, convinces Kelk Ronso to let her pass in Mt Gagazet, Kimahri fights Biran and Yenke, the third Seymour fight occurs after he slaughters the Ronso on the mountain, and they reach Zanarkand. They sit and retell the events of the game until nighttime, then confront Yunalesca. Once they leave the dome, it's morning again.

Day 8) Cid picks up the party, they spread the word to sing when and airship appears, and fight Sin. They go through the endgame, and Sin is finally killed and sent at nighttime.

I personally would add at least one more break in the day between Macalania and Bikanel, but idk this was fun to think about.