It’s possible to interact with dapps without going through a centralized server, for certain types of client hardware. Definitely not for mobile devices.
This would require more than just a mobile device, however. Perhaps a rooted Android device could self-host an Ethereum node, although your battery life may take a hit.
I think there are other chains and wallets that are designed around mobile use cases, which make it easier than on Ethereum to sync the whole chain, or use technical means to mediate the need to do so.
https://ethereum.org/en/developers/docs/nodes-and-clients/ru...
https://docs.flashbots.net/flashbots-protect/rpc/quick-start...