There are/were plenty of British YouTuber's doing "how cheap can you eat" meals through COVID and the cost of living crisis, they started at ~£1 for a bare-bones meal for one, they were at ~£1.50 last I looked; that's hopefully improving with the recent falls in inflation, but still and issue for many.
Of course the same demographic who can't afford the ingredients to cook their own healthy meals can often also not afford the time to prepare them either; due to working long hours, not being able to afford care for their children, etc.
Food banks are very much on the rise in many parts of the UK[0] and we have millions of children in poverty[1], a significant and heart breaking statistic for such a country.
[0] https://www.trusselltrust.org/news-and-blog/latest-stats/end... [1] https://cpag.org.uk/child-poverty/poverty-facts-and-figures
I understand the issues with sugar, I have no arguments with it, but it is, as you say, a blunt instrument. Sadly, the opposite case; healthy food, is also too expensive for the same demographic this affects; that's a separate and independent problem though, and the evidence in OP seems to suggest the tax is (somewhat) effective, so, again, no arguments from me.
EDIT: To be clear, I'm talking about in the UK when I talk about a demographic.
Making unhealthy food too expensive for poor people is a blunt instrument of course, but it does have an empirical case.
https://www.bmj.com/content/356/bmj.j163#