Any of the major SaaS integration services would probably be suitable — Zapier, Integromat, maybe IFTTT, which I’ve not used extensively. There are literally dozens more; just Google “alternatives to” any of these three to get started.
What you’ll probably have to do is define a group of views filtered to display trouble tickets at each level of escalation and then use the integrator’s ‘new record in view’ trigger; there’s no way to trigger on an arbitrary change in status. You’ll also most likely find the service loses visibility of tickets that are escalated and then de-escalated, as most (all?) services can’t catch a record’s second (and subsequent) entry into a view.
As far as notifications go, any of these services offers integration with a frankly stupefying array of messaging and notification services; somewhere out there is one right for your need and wallet. You may also want to look at the current suite of Airtable Blocks. While I’ve no direct experience with them, there are several directly supporting automated or assisted contact and notification from within Airtable. While I’m not sure which, if any, can be triggered by an integrator, they could at least provide contact functionality for your technicians to use directly.
[Weirdly, I envy you: I first became truly involved in management system design and integration by whaling on Sprint/Telenet’s old data trouble ticketing system, seeing what Quality Management miracles one might wring out of its data. (To give you an idea both of how long ago this was and how deeply enmired in it I was, I wrote my own virtual memory manager to let me manipulate — horrors! — datasets measuring several whole megabytes on a PC with 640kb of RAM.) For years, I kicked around the idea of trying to build a commercial trouble ticketing system some day — until it dawned on me that they, like the ‘big iron’ network management beasts I later helped design and build, just don’t exist anymore…]
