I do think you're right that more subtle nudges are probably fine. Some might begrudge them but such promotions are a lot more tolerable than directly pulling an entirely separate app into your existing app and then placing the newly imported bits in the spotlight.
I think there's huge pressure to "everything app" very disparate services. I've also noticed that Amazon now lets you pull up your Whole Foods code or pull up the Whole Foods storefront from the Amazon app.
My initial claim only works for Uber Eats. It can only be used for ordering food. There's a button to order a ride but it redirects to the Uber app.
But I believe you're right that initially they were more separate entities, but now it's kinda merged.
Honestly, I think this could go much better if they just organized their damn software better and not damage their music offering with forced podcasts. Many of us would probably stay loyal and use it for podcasts as well if they made the experience great instead of forced.
I think a good counter-example is Uber, with a separate app for ordering rides (Uber) and for ordering food (Uber Eats). Both apps are still bolstering each other by the brand recognition.
Additionally, the apps could still cross-reference each other in a subtle way. E.g. maybe when you type a podcast name in the regular Spotify it could redirect you to the Spotify Podcast app. Just like the Uber app sometimes nudges you to also order food.