You might look at the Logi MX Mechanical Mini or the NuPhy Air75. They both have Mac keys although I don’t think the top function row is exactly the same as a Mac keyboard on either. They also both have options with Brown switches. I have the tactile version of the MX Mechanical Mini and it’s pretty quiet but it’s still much louder than a normal keyboard IMO.
If mechanical is a requirement, there’s nothing to stop you building your own… Then you can have whatever keys and switches you feel like. [Hard to do that under $100, and it’s not complex, but does take time if you get stuck.] Not all keysets include Mac keys, so you have to plan carefully (or think creatively, e.g. using pictorial keys for Mac-specific buttons).
I’ve been using this for a few days and it feels great; thank you for mentioning it! I’d also been wanting “magic keyboard except mechanical” for awhile and bounced off some other options. So far the wifi receiver feels functionally equivalent to wired, like a Logitech does.