You need to reboot Windows for the DPI scaling to change. (You'll see parts of the OS itself need this as well; for example, icons on the desktop will be the wrong size until you reboot.
Mixing different DPIs on different monitors also introduces several OS-level bugs as well as other complications, but generally speaking you probably just need to reboot after connecting the monitor if it is set to a different DPI.
This assumes it is made the primary monitor, which is the one that determines system DPI. You generally always want the monitor set to the highest DPI scaling to be the primary monitor, so everything is rendered at a higher resolution and scaled down for some monitors, rather than vice versa.
Note that none of this is specific to Opus; it's just how DPI scaling works in Windows. Also note that Opus is DPI-aware but not multi-monitor-DPI-aware (very few things are), as the API for that just isn't ready yet. This means Opus will scale to the "system DPI" which can be any DPI that you set, but is the same across all displays. (This is different to apps which are not DPI-aware at all, which render at 96 DPI / 100% scaling and then get scaled to the system DPI or monitor DPI.)
Windows itself isn't ready for multi-monitor-DPI, in our opinion, given all the bugs that mixing monitors at different DPIs introduces into the OS itself. High DPI is generally working well now (with a few issues still remaining in the OS itself), but Microsoft's support of mixed DPIs is still very much evolving.