Just a few weeks after the film directed by Shawn Levy started shooting, the actors strike begun, so production had to be shut down until the conflict is solved.

... Excerpt from Deadpool 3 Likely Delayed, Missing From Disney's Calendar:

While they seemed to be rushing to very close to completing production before the actors went on strike last month, it now appears possible Deadpool 3 will not hit its original release date. During a call with investors yesterday, Disney presented a number of their big, upcoming plans -- and Deadpool 3 was nowhere to be found on the calendar. Currently expected to see release on May 3, 2024, Deadpool 3 is absent from a theatrical release calendar which runs through the release of Inside Out 2 in June. Disney did not comment on the change yesterday, and nobody seemed to catch it at the investors call.

Comic Book Movie picked up on the move, though, calling it to the attention of fans and social media. Whether and when Disney will make the delay official is anybody's guess; at this point, they haven't said anything at all.

There is probably an argument to be made that a delay could be good for Deadpool 3. If they have a chance to do reshoots after the strikes are over, not only will they be under fewer time constraints, but star Ryan Reynolds, a member of the Writers Guild of America who was unable to perform writing duties on set during the initial production, could presumably inject some rewrites into the production.