Pine needles are a great mulch resource. And though it’s a little hard to tell where your bed ends and the lawn starts, here’s some information for you to consider:

First, you’ll want to mow the leaves and pine needles as best you can to break them down and keep the leaf accumulation from smothering the grass below. This article explains more:

https://www.canr.msu.edu/resources/mulch_leaves_into_turf_for_a_smart_lawn

Additionally, the article below talks about the many benefits of using pine needles for mulch (though it addresses garden beds primarily, not lawn). But it may address any concerns you have with leaving the pine needles as is.
https://extension.unh.edu/blog/2019/10/do-pine-trees-pine-needles-make-soil-more-acidic

If you’re concerned about the depth of the pine needles in the lawn, you can consider raking them into the tree bed, or collecting them and spreading them on any other garden beds you may have. But there’s no harm in leaving them - the new grass growth in the spring will simply grow through the pine needles, and they’ll eventually break down.

Lastly, if you’re up for an experiment, you can try both methods in different areas of your lawn and see which result you like best next spring!

Thanks for Asking Extension.