Not sure if Alcaraz is also ready by that time, but I think he will be the biggest threat for Nadal this year in French Open.
Tsitsipas will actually be Nadal's strong competitor at the French Open. He failed when defeated by Djokovic and also Casper Ruud has the opportunity to trouble Nadal to win the next GS, this is just my thought, the most important thing at the French Open is never to let Nadal reach the final because of that like a certainty for this king of clay to win.
Regarding Nadal's injury
I quote statements from his social media that Nadal's injury is not too serious
It was a level 2 injury to the psoas iliacus muscle in the left leg. Nadal also said he would rest for a while for his recovery which is estimated to take 6 to 8 weeks.
That means Nadal will recover before the 2023 French Open next May.
This is good news for his fans and an opportunity for him to win the 23rd GS.