I asked this on MoT Twitter for a bit of a fun.
testability is define like a product is how easy it is to test, based on something criterias like a how you know the system, complexity and easy understanding.
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OH !! i like your definitions, very completed <3
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(Apologies if the above quote is being attributed wrongly … if was Heather’s quote of a Twitter post here: https://twitter.com/LearnsSolar/status/1103621605614329856)
Mr Bach’s document on testability definitely helps give/broaden perspective. I think that before I read his document I was aware of intrinsic testability (it’s the most intuitive, at least to me, of Bach’s testability types). About it he says the following:
“Observability.To test we must be able to see the product. Ideally we want a completely transparent product, where every fact about its states and behavior, including the history of those facts is readily available to us.”
“Controllability.To test, we must be able to visit the behavior of the product. Ideally we can provide any possible input and invoke any possible state, combination of states, or sequence of states on demand, easily and immediately.”
If I had the above in my test job I’d be a happy tester.
Highly encourage a full reading of Bach’s document to interested folks as it’s got a lot of really good stuff in…
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Testability for me (now) is the ability to me as a software tester to be able to see the implications and effects of my actions in a clear and easy way and hopefully not misinterpreting the results.
You want to be able to interact with the software with any tools necessary; tools being other software, hardware, body parts, blunt objects etc.
In the lower level the code should be testable with unit testing tools. On the middle layer you should be able to use the integrated and mocked interfaces to verify the functionalities.
Overall, the ability to monitor the software behaviour and get the logs out when needed without causing the performance and functionality to alter.
That, plus everything else in this chain 
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It is the set of planned and systematic activities applied in a quality management system so that the quality requirements of a product or service are met. Among these activities are systematic measurement, comparison with standards, process monitoring, all activities associated with information feedback loops. These activities contribute to the prevention of errors, which can be contrasted with quality control, which focuses on the outputs of the process.
A recent post by someone who is taking this challenge now
I know I am bit late but I recently got to know about this challenge 
For me, testability of a system defines how easily it can be divided into sub-systems and then verified.
If a system has high degree of testability then the coverage of testing area will be high and there will be more chances to uncover bugs in the system.
As we are approaching SHIFT LEFT, another aspect of testability is how early a system is available to test so that bugs can be identified in early state rather than when the system is on production.
I believe testability is how easy a product/system is to test.
My definition may change by the end of this 30 day challenge.