How to approach this? Fallen cypress seems like it’s “suffocating” Chinese privets. Also lots of half dead half alive mangled brush

This is in our backyard, southeast Texas. There is no danger to humans, I’d just like to responsibly clean it up to where I’m not damaging the ecosystem. I love these privets, and it seems like they’re being smashed down by this dead cypress that was struck by lightning. Is there anything I can do to help open the area up responsibly/safely to give the privets more room? Or just live and let live? And what to do about the half dead half alive brush piles?