Audio Hijack 3.8.0 is fully compatible with Big Sur, but for some reason, you've got to go to the update notes on Rogue Amoeba's website to find out...
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Full MacOS 11 (Big Sur) Compatibility
Audio Hijack now has full compatibility with MacOS 11 (Big Sur), with no known issues.

The new Great Equalizer is the SEND button.

In Memory of Harv: Those who can make you believe absurdities can make you commit atrocities. ~Voltaire