In the most abstract, opening up mobile and messaging platforms is a Good Thing. Unfortunately it is going to cause a mass of real world problems and will have significant negative consequences.
Requiring alternate App Stores will mean Facebook, Epic (Tencent), TikTok, and Scams R Us will all set up their own app stores. Their apps will slowly move to those stores where there are zero restrictions on the collection of personal data. Even if the OS requires user permission to access personal data people are just going to smash that accept button like they've been conditioned to do with GDPR dialogs.
Forcing alternate browser engines will just see Google use its enormous influence on the web to coerce everyone into using Chrome. The current "web standards" are ridiculously complicated. Google's "standards" are also privacy nightmares as they're perfect for fingerprinting. Web standards have gotten so complex Microsoft threw in the towel and just uses Blink. This legislation is just going to accelerate a Blink (and thus) Google monoculture on the web. If Microsoft can't maintain a viable browser engine against the complexity of web standards, driven primarily by Google, there's no hope for a plucky upstart to come along with a new browser engine. I guess learn to enjoy WebIrisScanner and WebAttention APIs when they're rolled out to help Google's ad business.
Messaging interoperability is going to be a clusterfuck. Messaging protocols and back ends are complex. The law doesn't seem to specify what messaging interoperability means at an implementation level. It's going to impose a huge cost on all messaging platforms to carry (and spool for delivery) traffic from third parties. While obviously the EU wants to impose cost on US companies, EU mobile carriers will end up subject to these laws and need to spend money supporting Facebook and iMessage traffic.
If history teaches us anything about sweeping technological regulation it's that we're not pessimistic enough about unintended consequences.