As a dumb example, when XMLHTTPREQUEST hit the streets, it was a paradigm shift in enterprise, but a pretty easy one for web developers to add to their toolbox. Years pass.... When everything became javascript, that was much harder, especially for the .Net folks who came from a VB6 background rather than a pure HTTP/TCP/CGI background. Lots of companies are still in infancy with adoption of modern front ends, mostly because their programmers are not polyglots and actively resist learning new things... and you can't just abandon hundreds of legacy apps through hiring better educated, modern web developers with the limited budget most companies have.
A few years ago we made a decision to shift from a .Net (+MSSQL+JQueryUI) stack to a Java stack, mostly for licensing cost avoidance after MS raised the price of SQL Server dramatically with 2012. More than three years later, >90% of our internal apps are still .Net and only a handful have been released on our new preferred stack (Java/PostgreSQL/Bootstrap/Angular) and probably only 10% of the programmers are competent enough to work independently using the new tooling.
This sad state is an area where there's a lot of naivete among young programmers and startups. The corporate world just doesn't work in remotely the same way. ... ironically, a lot of "progressive" corporations end up creating mini-Innovation teams internally with their best & brightest, who are told to "act like a startup" and end up basically creating 75% of all the new stuff ... until it requires an interface to a legacy system and the devs outside the team refuse to cooperate out of fear.
Oh, it's a mad, mad world.
I've been in exactly that situation, working on a small 'startup' team inside a large, traditional organisation. The friction between the 'old' and 'new' camps was heartbreaking.
This was after I'd moved on, but I'm led to believe that things have improved greatly since that change.
While I'm certainly stronger in one language I'd say it's quite normal to use at least 3 programming languages daily. As a Unix guy it's even more. If I just want to write a Python hello world I need to know some Python, some Bash, some Vimscript, some Terminal I/O. Many of my projects also have Makefiles, additional bash scripts (which includes SED and AWK besides Bash). Interaction with databases, APIs, JSON or XML or INI configs, HTML, etc is also common. And let's not forget that most systems that have grown over the years have a few DSLs to interact with their tools.
So before I finish my first coffee I've probably used 6 languages already on a typical work day. I think most coders in my company are fluent in at least 10 programming (&related) languages. And while our software development team is certainly better than my last gig I still hope it's not the top of what software dev teams can be.
And your most prevalent point is that company enforces some language usage. It's often not the same if you switch. So if you have more than 5 years you probably can increase the typical programming language fluency about 50%.
Also your example about switching stacks. Your first stack had .Net, C#, SQL, JS and JQuery. Now you at least sometimes also use Java, and whatever Bootstrap/Angular require.
I got fed up with this state of affairs a few years ago and stopped looking for .Net or Java developers and started looking for self-described hackers, assuming that would increase the odds that they had some passion for programming and could/would/had pick up whatever tools they needed for the job. It has worked well.
As an aside, though, especially in countries like India, Brazil, Mexico, Chile, Bulgaria, Poland, and others which are low cost recipients of outsourcing dollars, "software factories" are common, and in places like this it absolutely is common for an individual programmer to literally spend their time all day, every day doing the same one type of thing. Imho, the higher the CMMI number, the worse this gets (the pinnacle is the "just write a function to pass this test. No, it doesn't matter what it's doing or what this software is for. Just pass the test.", where developers on the front line are plug & play cogs who don't even know what they're working on).
I would consider a polyglot as able to express a full domain of ideas in multiple languages. (For example, knowing latin for biology or religious recitation doesn't make you a normal polyglot, while being able to use it at the breakfast table does.)
So, only if you are one of the few who regularly enjoys the thrill of forcing SQL to do your general computations, would it count in my book towards making you a polyglot in the context of general purpose computing. Similarly, how you choose to use shells would determine whether they count and whether they are each distinct.
The irony is that one of my Java friends told me that he could pick up any language on a need basis, and that I was ignorant for not knowing design patterns such as Factory, Visitor, Observer/Observable, etc.
Back when I was learning, I had Timex 2068 Basic and Z80.
Then at technical school, each class had its own programming language.
Followed by CS degree, with loads of programming languages.
First job, TCL, C, C++, JavaScript, C#, Java, SQL dialects.
Every single job afterwards required proficiency in multiple languages, even JVM/.NET (interaction with OS, languages that target those runtimes).
Timex's Basic really only added a few extra commands (on err, stick, delete, free, reset and sound IIRC.) Everything else was identical.
However the demos for the sound chip were great.