Google Photos is probably the best solution for you if you want to keep things simple. With 15,000 photos you're basically unlimited with the free version (with compression), because older Google accounts still have the generous "Storage Saver" option. If not, you pay relatively little for extra storage - usually around 2-3 euros a month for 100 GB, which is totally sufficient. The thing is simple: upload, available everywhere, and your photos are safely stored.
iCloud is honestly expensive if you need more than 5 GB. For you that would quickly cost 3.99 euros a month (50 GB) or more, depending on how it grows. That adds up to significantly more than Google over a year. However, iCloud has the advantage if you're living in the Apple ecosystem anyway and everything syncs seamlessly. Synology, on the other hand, is a completely different category - that's for people who'd rather control everything themselves and are willing to invest in hardware. You need a NAS device at home for that (from about 200-400 euros), and then you sync your photos locally. It's secure, but also more work to operate and not as convenient if you want to access your photos on the go.
My recommendation: go with Google Photos. It's cheap, reliable, and exactly right for your situation. The encryption is solid, and even if you later need 200 GB, it won't break the bank. Synology is more for people who need a lot of storage for family or bigger projects and are more tech-savvy.