I believe there might be problems with older versions of Safari. I don’t think it’s possible to upgrade Safari to the latest version except by running a newer version of macOS.
For what it’s worth, future major versions of Dorico will not run on versions of macOS earlier than macOS 12 Monterey (and I expect that only macOS 14 Sonoma and macOS 15 Sequoia will be officially supported), so it is probably getting towards time to think about an upgrade to a newer system. I know Macs are expensive, but today’s M4-based Macs offer incredible performance for their price.
Of course you should also do a complete audit of your system to check whether all of your mission critical packages can run on the latest versions of macOS.