I always separate them to app.*.com and *com. It makes things much easier to maintain and is a common approach.
Plus, my landing is usually Next.js on Vercel, and my app is Rails on Heroku, so I cannot really make them on the same domain.

The only downside is analytics; you have them separate. But I use Plausible, and after some tweaking, you can find a pretty good approach and see the user journey.