Also, the GNSS software in most phones is sadly unable to accept the correction data from any of these systems, regardless of whether it's a nationwide network or your personal setup. This is purely a software limitation on the vendor GNSS stack, but sadly there is not enough demand for this. (An app will not fix this, we're talking vendor specific low level system code here.)
[¹] e.g. u-blox T/R series, but check specific descriptions about raw output/RTK capabilities, it changes between generations. You also want recent ones with RTCMv3, not RTCMv2.x.