iMac as external monitor

27" 2560x1440 displays used to be really expensive. When the first 27" iMac came out in 2009, a standalone 27" display from Dell went for $1000 (when on sale) to $1200 (when not on sale).

These days you can get a 27" 2560x1440 or 27" 3840x2160 (4K) monitor with an IPS panel and near-100% sRGB coverage for as little as $300 – $350. It would cost $80+ to make a Thunderbolt connection from a M3 MBP to a 27" 2011 iMac even if Apple had not removed support for TDM from recent Macs and versions of macOS. Best to save the $80+ and put it towards purchase of a real monitor.

To keep it very short, NOPE that will not work. If your MBP needs an external display the best option available is to simply buy one and connect it. If you don't have any other needs for the 2011 iMac then you may want to consider using one of Apple's free recycling programs, you can find one for your part of the world in Apple Recycling Programs.

Why an external display:

• Simple setup that needs no tweaking
• Dead reliable
• Does not require expensive cabling
• Inexpensive (external display are available below $100)
• No expensive software to buy and maintain.

No. Your MBP is too new.

there are third party non target display options though

the performance is likely worse that target display at least with the wireless options

also your imac would be using a lot! more power than if you just bought an external 27" monitor

Use iMac as monitor: 5 Solutions - 9to5Mac