Advice please: First year teacher here. What steps should I take?

I'm a CISO for a very large school district, they definitely will not be able to see anything on your home network that isn't the chrome book.

The most likely have web content monitoring installed on the Chrome book to log and block websites visited on those. But really that depends on I'd the did it at the host level or the network, if the host. Then it's on your chrome book and anything you on that will monitored. If the network, then anything on the wifi can be monitored from a internet stand point, even your phone and MacBook. However things you do only on your devices can't be seen. Also, it more monitors what websites you visit, not necessarily what you do on them (e.g. it knows you visited Gmail, but won't have copies of your personal emails nor will it know what you typed. It will know you visited your bank, but won't capture account information, etc.) .

Keep in mind, school districts have extremely tight budgets. They neither have the interest not resources to spy on teachers or even students. Their intent is to 1) make sure students are safe online (not visiting porn sites, not downloading malware, etc) and 2) keeping their network and student privacy safe. They don't want student data leaked outside the network, they don't want to get ransomwared, etc. They definitely aren't spying on you or putting your privacy at risk. It takes a lot of resources to do that and I guarantee the school district doesn't have those resources. So yes, there is some personal privacy concerns, but IMO, none that are orwellian or egregious.

I primarily work from home doing IT for a hospital. My work laptop is for work only and in my router (Ubiquity Dream Machine) it doesn’t have access to my local network. When I’m on site I do connect my phone to WiFi, but use Proton VPN so they can’t see much more than that my phone is connected. This is overkill, but makes me feel better.

Work machine for work, home machine for home is the common mantra on this subreddit. But if you are allowed to use your personal machine on their network, I don't see the issue if you are not breaking any of their rules. They will not have monitoring software on your personal machine, so they will only be able to see the domains that you visit and not the actual pages.

I would, however, be very careful of any publicly visible social media profiles. Make sure your personal life is hidden as far as possible from students. Make sure if they search on your name, they don't stumble on embarrassing content.

Only use your work device for work, that's it. You're fine connecting to wifi but better yet would be setting up the guest network option on the wireless router, that way it doesn't talk to anything else on the network.

If you use your real name on Facebook/Twitter, then don't post anything that could possibly alarm or piss off parents (especially woke parents). Go through your accounts now and clean them up.

Treat the chromebook as a trojan horse / surveillance device- which it is. Use it as little as possible and wrap it in aluminum foil when not in use.

https://www.survivalsullivan.com/using-aluminum-foil-for-faraday-cages/

Also the EFF's anti-surveillance tips for students likely are also applicable to teachers:

https://ssd.eff.org/en/module/privacy-students