I am using CentOS 7.9 and I encountered the same problem after following instructions here to install and run gcc 11. I tried launching different versions of gcc and found only devtoolset-9 works, which corresponds to the file devtoolset-9 in /etc/scl/conf/ folder. So I copied devtoolset-9 to devtoolset-11 in the same folder, and gcc 11 gets working.

This issue in this case is RedHat subscription channels. Though the subscription and software are free (provided you have an active subscription already), for some reason you have to make a 'special request' to RedHat as per:

https://access.redhat.com/solutions/472793

You can automate this by visiting:

https://www.redhat.com/wapps/try/RHSCL

(when logged into the support portal). This should automatically be approved after which you can attach a new subscription. Identify the pool id using:

subscription-manager list --available --all

To find the pool id:

 Subscription Name:   Software Collections and Developer Toolset
 Provides:            Red Hat Developer Tools (for RHEL Server)
                      Red Hat Developer Tools Beta (for RHEL Workstation)
                      Red Hat Software Collections Beta (for RHEL Server)
                      Red Hat Software Collections Beta (for RHEL Workstation)
                      Red Hat Software Collections (for RHEL Server)
                      Red Hat Developer Tools Beta (for RHEL Server)
                      Red Hat Developer Toolset (for RHEL Workstation)
                      Red Hat Software Collections Beta (for RHEL Client)
                      Red Hat Software Collections (for RHEL Workstation)
                      Red Hat Developer Toolset (for RHEL Server)
                      Red Hat Developer Tools (for RHEL Workstation)
                      Red Hat Software Collections (for RHEL Client) 
SKU:                 foobar 
Contract:            1234 Pool ID: XXXXXXXXXX

Then attach this and enable the newly available repos:

>subscription-manager attach --pool=XXXXXXXXXXXXXXXXXXXX
Successfully attached a subscription for: Software Collections and Developer Toolset
>subscription-manager repos --enable rhel-workstation-rhscl-7-rpms
Repository 'rhel-workstation-rhscl-7-rpms' is enabled for this system.
>subscription-manager repos --enable rhel-7-workstation-devtools-rpms
Repository 'rhel-7-workstation-devtools-rpms' is enabled for this system.

You can now install freely:

>yum update -y 
>yum install -y devtoolset-7-gcc-c++

Quite why they make you jump through so many hoops is explained by RedHat as follows:

-If you have a 2013 RHEL SKU with Standard or Premium service level, there should be no action on your part, and your subscription should have full access to RHSCL.

-If you have a 2010 or older RHEL SKU with Standard or Premium service level, you should contact Red Hat Customer Service to request the RHSCL SKU (and all related content) added to your account.

NOTE: Developer Toolset is now included as part of Red Hat Software Collections. This change was made on May 29, 2014.

As you had Red Hat Enterprise Linux Workstation, Standard subscription which is older RHEL SKU with Standard service level, you had to initiate a special request for it

To install the full tools-set including gfortran on centos 7:

yum install centos-release-scl
yum install devtoolset-8
scl enable devtoolset-8 -- bash

enable the tools:

source /opt/rh/devtoolset-8/enable 

you may wish to put the command above in .bash_profile

ref: https://unix.stackexchange.com/questions/477360/centos-7-gcc-8-installation

While Devtoolset-3 and 4 are located on the Centos mirror site, yum will not be able to find them as they were not included in the repodata on the site. These were probably excluded because they are EOL (end-of-life), and have dependency bugs (Bug 1410152). Try using the older Devtoolset-3 packages here, which do not have the dependency issues:

https://copr.fedorainfracloud.org/coprs/rhscl/devtoolset-3/

If you really want the packages from the centos.org site, I went with wget to download all the RPMs, then recreated a local yum repo. However, you'll see the dependency issues and yum install devtoolset-3 will fail.

$ wget -r -p -e robots=off --directory-prefix="/mnt/local-devtoolset3-repo" --recursive --no-clobber --no-parent http://mirror.centos.org/centos/6/sclo/x86_64/rh/devtoolset-3/
$ sudo yum install createrepo
$ cd /mnt/local-devtoolset3-repo
$ createrepo --database .