I don't have an end-to-end solution, but I will say as a former Pebble user that I'm delighted with my BangleJS watch. It's inexpensive, I charge it once a week, and it has the usual activity tracker hardware including heart rate monitor. There are a ton of apps. It's less "hacker" and more polished for non-technical users than you might expect; if you're running Linux, this is absolutely within your comfort zone. It also has a temp monitor, so it can detect when the watch it being worn or not.

The customized GadgetBridge Android app is good, most of the programming is in JavaScript, and the developer community is active and responsive.

A quick glance through the app "store" (they're nearly all free) shows there's a heart alarm app, which seems aimed at notifying the wearer. Another app publishes heart rate over bluetooth, so someone must have a pair device that monitors heart rates.

I didn't see anything obvious in the ecosystem, but since the data is going to GadgetBridge already, it's most of the way there; if GadgetBridge could publish to web hooks, with ntfy you could get alerts from watch to partner's phone. I haven't yet looked through the GB issues to see if someone has already requested it, and I've only done light digging in the app itself; it may already support this.

It's worth investigating.

Edit looks like others have requested similar features (and this, and this); it hasn't been implemented yet.