This isn't less accessible than a hamburger menu. Even the opposite might be the case as defacto most hamburger menus are implemented without proper focus handing or correct aria attributes for announcing open/closed states.
With the sausage menu, at least as screenreader user, you will have less issues as you can tab through a list of links immediately without the need to open a broken menu . Also scroll position is adjusted by the browser automatically to the element in focus, so it isn't even a problem for keyboard users with eyesight.
My job is to build frontends on top of various client management systems and figured out, that I get more maintainable code and am more productive using the templating of the CMS itself instead if decoupling the frontend from the CMS entirely.
So since two years, I use the Hotwired stack on top of PHP (and now with Vite as bundler) and that is so far the best solution I found. I can like use the CMS integrated solution for handling forms, as an example, but can plug in Hotwired Turbo and some Stimulus controllers when I want things to happen async on the client. I now have my own set of generic stimulus controllers I reuse in every project. But at the end of the day, those websites work without JavaScript.
I didn't try to convince anyone. I deleted it and people started to reach out on Signal, Telegram and Threema. A friend of mine did the same 4 years earlier and it worked out.
This probably doesn't just work for everyone, in every country. But look, people still use phones and these things actually have a phone feature. You might not be as cut off without Whatsapp as you think.
With the sausage menu, at least as screenreader user, you will have less issues as you can tab through a list of links immediately without the need to open a broken menu . Also scroll position is adjusted by the browser automatically to the element in focus, so it isn't even a problem for keyboard users with eyesight.