If the financial situation at P+ allows, they would be absolutely stupid not to do something with it - Picard S3 has been a bonafide hit, arguably their biggest mainstream commercial and critical success since Discovery rebooted ST (both in terms of ratings and overall acclaim). Its put P+ content on the streaming map as a serious competitor more than any other content they've produced, charting in the top 10 regularly up there with all the big household name streaming shows. There is talk of serious Emmy nominations. In short - its broken through with the masses, and a new streamer needs that to prove longevity.
They aren't gonna ignore that commercially or creatively. I'd expect at least a made-for-streaming movie or a mini-series to follow-on from it to capitalise on that success, even if just to test the waters for doing more. As a business, they're not gonna totally ignore the success they've enjoyed from this final season and not try to capitalise on it, even if done economically. The sets are all built, the cast are in - its gonna be a case of dotting the i's and crossing the t's, and perhaps even reviewing and changing their existing plans to enable funding for something to be done.
The only caveat will be the question of whether they can keep the momentum, capture lightning in a bottle twice, and if without the big draw of a TNG cast reunion it can capitalise on what S3 has started with anywhere near similiar levels of success. I suspect that how best to do that will be the crux of their thinking right now! My personal view would be to capitalise on any TNG stars who want to return for recurring/guest roles, but expand it out to all the 90's Trek to extend the "legacy" theme to all of the 24th century shows. Maybe make that long-awaited 24th century show mash-up for a movie, using the Enterprise G and Captain Seven as the platform.
That was a much longer musing than I set out to post! But I think the short answer is I have no doubt there will be "something" following up on and attempting to capitalize from the apparent success of Picard S3 - but what that "something" ends up being is up in the air. There will be "something" though, as it makes zero sense at all for P+ to not want that.