It likely won't affect the 2023 movie slate much, seeing as the edits of most 2023 movies are either locked or close to being locked, with only effects and sound and other non-editing post production left. The first hit will be scripted broadcast series in the fall, which traditionally start in September. ABC. CBS. FOX. NBC. Don't expect any more scripted content on those channels for the rest of the year. It'll then start to get dicey for cable/streaming series soon after. Some stuff will manage to be completed and released in the third quarter, but not a ton, seeing as so many productions have been shut down, and will continue to be shut down. In other words, the public won't feel anything this summer, but fall TV could get be pretty bleak.
Honestly, though, all that really matters is how much money the studios - and the local economy - continue to lose. And I think that's probably all going to come to a head by the end of the summer, before the public really starts to notice, especially if SAG strikes as well. That said, some people think the strike could last until October, but I personally think the governor and other big wig intermediaries will step in before then.