I downloaded .spk file for DSM 7 RoonServer_Synology_DSM7_x86-64_20220216 and tried to manually install it from Package Center and it says “This package is not supported on the platform of DiskStation or is incompatible with the current DSM version”
Is there any way of getting Roon core to run on my Synology DS1515?
No you need a compatible NAS instead. Anything that has not an Intel x86 or compatible CPU inside is not supported.
Because of incompatible CPU - no.
Funnily the DS1515+ has an Intel Atom which is theoretically compatible. But I would strongly recommend not to try roon on that one as it is painfully underpowered for roon. My experience with Synology NAS is in general that only current and really powerful machines can handle roon well.