Due to hardware constraints, 2011 iMac can run no higher than macOS 10.13 "High Sierra." Are you running that now?
98% of slow iMac reports here are the result of the mechanical hard drives of the era. In spite of that, an entry level 2011 iMac 21.5" scores 30% faster than 21.5-inch models from 2012 through 2019 with entry-level mech drives. Still yes, that feel slow. We also have a 2011 model still in use.
This is a simple test for the presence of the expected slow hard drive in an otherwise healthy old Mac:
- Is the computer slow to boot?
- Are apps, especially big ones, slow to open?
- Once opened, do the apps seem to respond acceptably?
Three "yes" answers = typical slow mech HD issues
As your only complaint as this point is only slowness, the external USB boot solution on a 2011 iMac will exacerbate the current problem and I can only recommend it if that is the only way to recover data. The limitation of your iMac's USB-2 ports, as Servant of Cats points out, is that an external USB 2 or a FW800 boot drive cannot run faster than about 1/4 to 1/3 the CURRENT speed of your internal drive, assuming the internal is healthy.
By the way, the 2011 iMac was the first to have 6GB SATA internal drive bus instead of the 3GB of the 2010 and older models. This is from our 2011 iMac 21.5:

The SATA "Negotiated Link Speed" is a clock-back from 6GB due to being connected to a 3GB SATA drive.
The SATA bus is 6GB but Apple used as 7200rpm 3GB hard drive. Realistically, had they used a 7200rpm 6 GB drive, the speeds would still be under 200MB/sec and that, today, feels slow.
The 6GB drive bus opens the path for an internal SATA 6G SSD upgrade that would do real-world speeds of ~500 MB/sec and feel quite snappy. However given that High Sierra is already losing browser support makes the labor + expense of doing the fast internal upgrade less attractive, and I cannot recommend you go that way except as a hobby/learning experience if you can afford that.