video_output: bring PrerenderPicture() closer to calling vout_display_Prepare()

As discussed in !7513 the API's called by the splitter should be similar to what the vout is doing in the core.

We can't do that yet with vout_display_Prepare() as it doesn't handle subpictures (there's a TODO). But the steps in this MR bring this closer and will be necessary no matter what.

It also avoids doing some things in the display lock.