Its going to at least extend through the summer at this point.
Even if the Shubert Org has a production that wants the Majestic, which wouldn't be able to load in until Spring 2024 with the renovations that have to be made to the theater once Phantom closes. I highly doubt any show that desperately wants the Majestic that they would sign a contract over 15 months out to guarantee it. I would understand if Phantom were playing a house like the Winter Garden, which has unique stage dimensions and optimal location that production would be willing to lock down a lease as soon as possible, as it happened with Beetlejuice by The Music Man. A production going into the Majestic on the other hand could just as easily go into the Shubert, Imperial, Lunt-Fontane, St. James, and arguably the Marquis with little if any modification to the shows production design. Add to that its as if the Majestic is in a more optimal location with additional visibility then the other theaters mentioned, that unless one of the shows in them is a massive hit, will all likely be in search of a tenant in Spring 2024.
So anyone saying that the Shubert Organization is not allowing Phantom to extend past April 16th, is buying the the BS Mackintosh is spewing. While the Shubert Organization is likely very eager to renovate the Majestic, they are also likely over the moon that Phantom is playing to packed houses again since it means their profits are also soaring. I don't know if Phantom's lease agreement is so old it does not include a cut of revenue as a part of rent, which is now standard, but they are likely seeing a massive increase in concession sales that do benefit them.
At this point if I had to suspect around the 35th anniversary we will see an announcement that the show is going to extend through end of Summer (August/Early Sept) announced as the "final extension". This additional 4.5 months of sales 9 months out would allow Mackintosh and Webber to see if Phantom has actually been given new life or the sales are only due to its imminent closure. Thus by June a final decision could be made if the late summer closure would indeed be final, or the production once again becomes an open run "DUE TO POPULAR DEMAND".