Target display mode
May I use my iMac 27 from mid 2011 like target display for my new iMac silicone M1 with Big Sure?
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No.
Target Display Mode is history, and although your 2011 iMac could participate you need another old Mac with 10.15 or earlier as its mate.
Apple's support document Use your iMac as a display with target display mode is specific:
The other Mac that you're connecting it to must have been introduced in 2019 or earlier and have macOS Catalina or earlier installed