A tool for managing user identities, credentials, and access across on-premises and cloud environments
Since it appears that Securly actually uses website filtering to monitor the network traffic to/from Internet servers including Google [Docs, Drive], YouTube and others, it's likely that any external website including Microsoft's will be monitored as well, which if you're using a Chromebook would be literally any app you use since nothing really operates locally on those devices.
This means there's simply no way to be certain that anything done on the device even from home isn't being monitored, which based on the Securly sales information is exactly what they promise to schools, so I suspect that's what they're doing even as you browse these pages at Microsoft.
If you're an employee, then trying to bypass such systems is stupid, either talk to the IT support or possibly a related teacher and staff relations group about what policies they have and what is allowed, or simply give up using your school device or in fact any devices from the school itself, since those are typically all filtered, and instead use your own device(s) from home for your writing.
The product was flagged by a school in the Milwaukee School district for its privacy invading design, among others who've commented on this privacy issue, so those school systems that actually use it likely don't care about your privacy, but only by asking will you learn whether this is the policy and whether you should even attempt this, since it's quite likely to be a threat to your employment if you do it anyway.
I'm a technical person by background and wouldn't even bother trying from what I've read. Get your own device and use it offline while writing if you're operating at school, always remembering that while online your website use is being monitored, along with any public online documents or postings you've made on social media or possibly other sites if you post your stories online as well. Keep those completely separate in a personal account at Microsoft, for example, with no public or even private access while operating at school, since that might likely be tracked and filtered to protect the school.
Rob