iMac as second monitor to old one

Same link I provided and it clearly says:

To use any of these iMac models as an external display:

• The iMac used as a display must have macOS High Sierra or earlier installed.
• The other Mac that you're connecting it to must have been introduced in 2019 or earlier and have macOS Catalina or earlier installed.
• The cable connecting the two Mac computers must be a Mini DisplayPort  cable.

Your 2010 iMac simply will not work as an external display. Please quit wasting your time. Target Display Mode is dead technology and Big Sur ( which is installed on the 2020) does not support Target Display Mode. Before you ask, no you cannot backdate the 2020 iMac to an earlier version of Mac OS.

In short, if your 2020 27" needs an external display you need to buy one. Please carefully read Target Display Mode (Target Display Mode).

We know this is not what you wanted to read but it is the truth, we your question multiple times per day and the answer is always the same.

By the way, you can find external displays that will work fine with the 2020 iMac for less than $100.

You can have a second display, you just can’t use the old iMac as one.

Writer26 wrote:

That's the opposite of what Apple just told me, so that's great. Thanks for the help.

Was it Apple personnel that told you that or Best Buy personel?

Welcome to the Apple Support Communities.

You cannot use it as a second display; the new iMac isn’t compatible with Target Display Mode.

Jack

No cable or adapter will work. iMac is a computer, not a display for other devices.

There are a limited number of Macs that had this functionality, but not yours, unfortunately.

It may be the opposite of what Apple told you, the rep you spoke to either did not understand or made an error.

Target Display Mode is dead, read Apple's official line in the link I provided you.

Well, that certainly is surprising.