Can I use a late 2015 iMac as a monitor for a 2021 MacMini or as a 2nd monitor for a 2020 iMac?

The problem is not with the 2015 iMac, the problem is that the 202X macs can't use Target Display mode. So you got bad advice.

https://support.apple.com/en-us/HT204592

"The other Mac that you're connecting it to must have been introduced in

2019 or earlier and have macOS Catalina or earlier installed."

Per the article you came from, 2015 is a problem as well:

TDM support in iMacs ended with the Mid 2014 model.

There is an anomaly at play. It does not involve the models you have but is likely why so many rumors debauched onto the internet when people were forced to work from home. Some 27" 2009 and 2010 iMacs were, by accident, found by users to work as a external monitor for some—not all— non-Apple devices included computers and even a few gaming consoles. Some even worked with Catalina on pre-2020 Macs set as the video source. But...

....this was never intended, documented, or supported by Apple. Yet this anomaly apparently became the model and justification for starving web journalists lacking integrity, basic research skills, or editorial help to make up stuff to fill out their "how to work from home," spoutings.

Unfortunately, a number of posts here since March 2020 reported basically the same conversation you had. It suggests that the journalistic flood of post-processed horse feed got to a few employees who did not believe Apple's own TDM documentation. People are human.

Target Display Mode is DEAD! You cannot use a late 2015 or later iMac for Target Display Mode. In addition the final nail in the coffin is any Mac OS after Big Sur (possibly 10.15.x) will NOT support Target Display Mode either. In short, if you have a need for an external display, please buy one. Macs are computers, they are NOT an external display for any other devices.

The advice you received was in error.

In addition to the excellent guidance provided above, you might take a look at this youtube vid discussing and demo-ing a new feature of Monterey; AirPlay to Mac. There's a small possibility that it may be useful to you.

https://www.youtube.com/watch?v=dNujbk9RJWc

While below is the note from Apple regarding the feature, according to the above linked vid there are apparent variations that will also function.

"Available on MacBook Pro (2018 and later), MacBook Air (2018 and later), iMac (2019 and later), iMac Pro (2017), Mac mini (2020 and later), Mac Pro (2019), iPhone 7 and later, iPad Pro (2nd generation and later), iPad Air (3rd generation and later), iPad (6th generation and later), and iPad mini (5th generation and later). Older iPhone, iPad, and Mac models may share content at a lower resolution to supported Mac models when “Allow AirPlay for” is set to “Everyone” or “Anyone on the same network” in Sharing preferences".

macOS Monterey - New Features - Apple Support

While Target display is dead, If both devices are running Monterey, you may be able to use Airplay to Mac instead:

Link-> https://www.youtube.com/watch?v=tDxk5GiBD7k