Thank you for these comments and for taking the time to look at my bundles.
Just one of the XSLT style sheets, ddb.xsl in DDB Access, requests version 2, but it is a critical one. As I mentioned above, I don't know if there is a specific reason. I just couldn't ignore it. Clearly, the main point is that I had no solution at all for iOS.
Using JavaScript was the first answer from Apple. I had not thought of this kind of solution. Later on, Apple had a second thought and suggested to use xslt rather than JavaScript.
My reference to an external C library some years ago comes from a very old comment in Stackoverflow #462440 (cf. discussion in the bottom). I am neither an XSLT expert nor a system expert, and it seems that finding the appropriate answer was not immediate. I regard libxslt as "unsafe in the medium term" not for security reasons, but because as you mention XSLT is not frequently used in this environment. From an Apple perspective, it can easily be removed if needed.
My lookup (detail) pages are based on WKWebView. I could actually get a first result with the most complex style sheet (ddb.xsl) in a few hours, with just a few lines of code. The most difficult point was to use correctly callAsyncJavaScript. It would be difficult to use evaluateJavaScript for transparency reasons, while callAsyncJavaScript takes care of the transparency.
I shall try to progress on this basis. If it works correctly, I shall save a lot of time.
Thanks again for your help.