v0.0.9 added support for beta 2, less than a day before beta 2 came out. (I compared beta 1 and beta 2 of Catalina, to make an educated guess about some of the changes Apple might make in beta 2 of Big Sur, and my guess turned out to be correct.)
I would expect v0.0.9 and later (the current version is v0.0.14) to work with beta 3, however I have not tested it myself yet. If you've tried it and you're having trouble, you may want to wait for the next patcher release (v0.0.15), probably sometime later today, before you spend more time and effort trying to troubleshoot. I found a bug in patch-kexts.sh (the script that runs in step 9 of the instructions) which doesn't affect anything most of the time, but which makes it incredibly difficult to notice if kmutil failed with an error. After I fix that, any problems with the script will be much easier to troubleshoot.
Edit: I forgot to mention, the bug has been around since v0.0.6, which was also the first version of the patcher that could do anything to fix WiFi, so for all practical intents and purposes it affects all versions of the patcher.
Edit 2: Apple added a ton of stuff to the
Big Sur beta release notes. In particular, it sounds like it
might now be safe to install Big Sur in the same APFS container as Catalina 10.15.6 (but not any earlier version) -- but look at the exact wording below in case I'm wrong -- and Apple finally documented the changes they've made to Time Machine.
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