Infrastructure monitoring tools like Nagios or much more "low-level" curl are well known in the DevOps community.
But, given I would like just to track some APIs in similar manner just in frontend, what are known more or less mature popular tools or components to support this functionality? i.e. like Nagios but running completely inside the browser (loading static configuration file from server together with the JS libs would be ok).
You have a few options for this:
If you can pay for this, use commercial API monitoring solutions like Runscope or APImetrics. They're easy to setup, have no maintenance overheads, and show you detailed data and alerting etc. The problem with this approach is that they cost money, and if you have a miniscule ops budget or this is a hobby project, it can be hard to justify spending on this.
...which brings me to the alternative: roll your own. If you have your own system monitoring and metrics setup (Nagios/Icinga/Sensu, and Grafana etc), you can write check scripts for whatever data you need (availability, response time or latency etc). Some of these tools integrate with time series databases like graphite/influxDB, so you can push the check data to that and use a visualization tool like Grafana to show graphs and charts based on this data (here's a blog post describing Icinga-Grafana integration)
I don't think there are any popular tools for doing this, because it's not a popular way of monitoring. Anything running completely inside the browser will only execute checks as long as it's open in a browser window, so it's not going to be a popular method of monitoring, full stop. It's just not reliable.
That said, it would be pretty easy to hand-roll something like this in a couple hours with simple HTML/CSS/JS. It might not be pretty, but it would meet the stated requirements.
