At 15,000 photos you really need a solution that actually scales now 😅 I've been through something similar - eventually the storage was full and I had to make a decision, and honestly the answer depends a lot on how tech-savvy you are and how paranoid you want to be about data privacy.
Google Photos with compression is honestly the most relaxed option for most people. You don't pay anything for unlimited compressed storage (the quality is still really good, not like back in the day with extreme compression), the search works incredibly well - you can search for "dog" or "beach" and it actually finds the right photos - and it works on Android, iPhone, everywhere. The catch: your data is with Google, and if you want original quality you do have to pay for storage. A lot of people think that's totally fine, some don't.
The Synology route (or other NAS systems too) is more for people who want to keep their data at home and have a stable internet connection. But you also need some basic knowledge - buying a NAS, setting it up, maintaining it regularly isn't complicated, but it's also not zero effort. In return you get full control, zero subscription fees in the long run, and your photos never leave your home. Though you do need a backup of that backup 😅 (a second external drive or something), because a single NAS is just a single drive.
My honest take: if you don't already have a tech setup at home, start with Google Photos. It's maintenance-free, available everywhere, and you don't have to worry about power outages or hardware failures. You can always switch later.