An update from Apple. Apple actually reversed that decision. Finally. Tested on latest stable version of iOS 17.4 and it works. (from https://developer.apple.com/support/dma-and-apps-in-the-eu/#dev-qa ):

Why don’t users in the EU have access to Home Screen web apps?

UPDATE: Previously, Apple announced plans to remove the Home Screen web apps capability in the EU as part of our efforts to comply with the DMA. The need to remove the capability was informed by the complex security and privacy concerns associated with web apps to support alternative browser engines that would require building a new integration architecture that does not currently exist in iOS.

We have received requests to continue to offer support for Home Screen web apps in iOS, therefore we will continue to offer the existing Home Screen web apps capability in the EU. This support means Home Screen web apps continue to be built directly on WebKit and its security architecture, and align with the security and privacy model for native apps on iOS.

Developers and users who may have been impacted by the removal of Home Screen web apps in the beta release of iOS in the EU can expect the return of the existing functionality for Home Screen web apps with the availability of iOS 17.4 in early March.

Finally, some good news.