Well, the question is theoretical, so will be the answer. In the form of a 2015 commentary (in Science) on the paper that seemingly first proposed this concept:
Vaccines have saved millions of human lives, but according to evolutionary biologist Andrew Read they sometimes may also cause pathogens to turn deadlier. Read first put forward the theory 15 years ago. Now, in a new paper, he presents evidence that that is what happened with the virus causing Marek's disease, an infectious disease in chickens. Read acknowledges that the effect has never been seen with human vaccines, but he argues that future vaccines that prevent disease rather than infection could have the same effect. Other researchers say that no general conclusions should be drawn from the paper. Even if he turns out to be right, the study offers no support whatsoever for those who oppose vaccination, Read stresses. If "leaky" vaccines are proven safe and effective, they should be used, he says, but perhaps with closer monitoring and additional measures to reduce transmission, such as bed nets for malaria. [...]
But other researchers say the study has
little relevance for public health. Read
“should stop scaremongering,” says vaccine
researcher Adrian Hill of the University
of Oxford in the United Kingdom. [...]
It’s a convincing study, says Michael Lässig,
who studies influenza evolution at the
University of Cologne in Germany, “But
it’s a very special set of circumstances …
I would be careful about drawing general
conclusions.” Hill also thinks that Marek’s
disease may be a special case; nothing suggests
that human vaccines have ever made
a disease more virulent, he says. What’s
more, natural immunity is “leaky,” too, Hill
argues, allowing infected people to survive
and transmit a disease that is deadly to
others. “For malaria, whatever today’s vaccine
does is a drop in the ocean of all the
immunity that is happening in Africa from
all the infections,” he says.
There's some more expert commentary on that 2015 paper.
“So, what have they shown? Put simply, they have shown that chickens infected with a lethal strain of the virus (Marek’s disease virus, MDV) can only transmit it until they die (whereas those infected with a non-lethal strain can transmit it over a prolonged period). If chickens were immunised with a “perfect vaccine”, it would both protect them and prevent them transmitting MDV to other chickens. Current vaccines against MDV, however, are “imperfect”, in that vaccinated chickens will be protected and will survive but will still be able to transmit the virus to other chickens (which will, unless they too have been vaccinated, die). Vaccinated chickens therefore present a mechanism for prolonged shedding and transmission of the lethal virus.
“What have they not shown? As the authors acknowledge, they have not demonstrated evolution of MDV from non-lethal to lethal forms in vaccinated chickens. Their work does, however indicate that, if such a mutant virus arose, it could be maintained in chickens vaccinated with the “imperfect vaccine” but not in unvaccinated chickens.
So, in other words, the putative evolution of the virus hasn't really been demonstrated in that paper. Not sure how you'd expect it to be proved or disproved for a human-hosted virus, if doing that for one that infects animals is so difficult...
And by the way, the "leaky" term is not really that widespread... because a number of researchers disapprove of it:
“A word of warning on terminology – the authors use various terms to describe the vaccines: “sterilising” versus “non-sterilising”, “perfect” versus “imperfect” and “leaky” (versus presumably “non-leaky”). Apart from the matter that technically it is the immunity induced by vaccines that is “sterilising “ or “non-sterilising”, the term “leaky” is to me the least desirable as it could be seen to imply an implicit defect of the vaccine, which could be translated by some as meaning that the vaccine itself poses some threat – this is not the case.”
On the other hand, there are some recent reviews (e.g. Milller & Metcalf 2019) that are more favorable to Read's hypothesis, and find some corroborating evidence from how (imperfect) natural immunity affects virulence) although as I mentioned the "leaky" terminology is not favored.
Read et al.  showed
convincingly that when vaccines blocked the mortality effects
of Marek’s disease virus in commercial poultry the virus
evolved higher virulence to the point where vaccinated hosts
lost all benefits of vaccine-induced immunity and non-vaccinated
individuals experienced increased mortality. Recently,
Fleming-Davies et al.  showed that incomplete acquired
immunity (analogous to vaccination) to the bacterial pathogen
Mycoplasma gallisepticum in finches selects for increased virulence,
as low-virulence strains are unable to infect previously
infected hosts while high-virulence strains retain this ability.
[citing 17]: Fleming-Davies AE, Williams PD, Dhondt AA,
Dobson AP, Hochachka WM, Leon AE, Ley DH, Osnas
EE, Hawley DM. 2018 Incomplete host immunity
favors the evolution of virulence in an emergent
pathogen. Science 359, 1030–1033. (doi:10.1126/
What I would call false however is any attempt to imply that only vaccines can cause this effect. As Fleming-Davies et al. put in the conclusion of their paper...
The effects of incomplete immunity described here are arguably a specific case of a broader phenomenon whereby increased virulence is favored by quantitative host variation in susceptibility, whether due to host genetic variation, imperfect vaccines, or innate immune priming.
A bit more searching does find one preprint that discusses via modelling/simulation how it might apply to SARS-CoV-2... apparently it doesn't based on the title "No current evidence for risk of vaccine-driven virulence evolution in SARS-CoV-2". I'm not up-to-speed with the research on how the Delta variant might have arisen, but for the "Kent" one it's been suggested/suspected that it came about in an immunocompromised individual (no vaccine was suggested to be involved) due to the number of accumulated mutations.
And since you name-dropped Bossche, he's selling [at least as an idea] some kind of "universal vaccine" holly grail that doesn't currently exist, and probably can't really exist either. He should not be really confused with Read though; as far as I know the latter is more reputable researcher...