For what it's worth, the 'shy Tory' effect isn't really a thing, at least in British opinion polling. Maybe in the 1992 General Election, when it was coined, not since. Polling errors go both ways, most polling misses turn out to be a result of turnout modeling problems or (occasionally) unrepresentative samples, and voters have no problem at all telling pollsters they're going to vote for the Tories, UKIP, or anyone else.
Take the present prime minister. I don't think it's particularly controversial to say that he's repeatedly proven himself to be a fairly brazen liar. Voters don't actually like liars. They do, nevertheless, like Johnson (and quite a bit more than they like Starmer). And they're not shy about saying so.
I gather that it was still an active phenomenon as of the GE in 2015 [0][1], and in 2016 there was a significant underestimation of the Leave vote [2]. I'm not really sure how the last part is supposed to relate to this issue in particular, other than being a general swipe at BoJo.
There was a fairly large polling miss in 2015, yes - and the traditional in-depth postmortem by the British Polling Council[0]. Nevertheless, the conclusion from the inquiry was that the shy Tory effect "...is unlikely to have been a contributory factor in the polling miss." (p.42). Or from your link 0: "I do not mean to dismiss the "shy Tory" argument out of hand, but I find it far less plausible in 2015 than in 1992".
In short, the polls are normally a bit wrong, and sometimes more than a bit. And occasionally that changes the expected result (as in 2015) rather than just the magnitude of an expected victory. And over the last 30 years or so those misses have on average been larger against the Conservatives than against Labour. But the conclusion, on analysis, is that the misses have generally been caused by structural problems with the polling, not respondents lying because they're shy. This shouldn't surprise us too much: trying to produce a valid poll with less than 100% response rates requires assumptions, and increasingly more heroic ones as the numbers fall and distributions of those still answering change. I'm mildly in awe of my colleagues for getting as close as they do, given how difficult the problems are. And (with the exception of a few partisan hacks) the polling industry and polling academia in Britain is remarkably straightforward about exposing their errors in public and issuing 'mea culpa's where appropriate.
The last part was intended to relate because the notion of a 'shy Tory' is that a voter has deeply-held but perceived socially embarrassing views that they are shy about revealing to a pollster. Persistent dishonesty is disliked, by voters of all parties, and seen to be socially unacceptable - so we would expect social desirability bias to apply to polling for Johnson. But, in fact, voters are happy to rate him as both dishonest and their preferred choice for Prime Minister. Which suggests in a straightforward (though admittedly non-rigorous) way that they're unlikely to be hiding voting for his party.
Take the present prime minister. I don't think it's particularly controversial to say that he's repeatedly proven himself to be a fairly brazen liar. Voters don't actually like liars. They do, nevertheless, like Johnson (and quite a bit more than they like Starmer). And they're not shy about saying so.