You can use the sdk-manager sdk search subcommand to search for available SDKs separately from the toolchains.
For example, the following command uses the v3 substring to filter all SDKs from the v3.0.0 upwards:
> nrfutil sdk-manager sdk search v3
Type Version Status
nrf v3.2.1 Available
nrf v3.2.0 Available
nrf v3.2.0-rc2 Available
nrf v3.1.1 Installed
nrf v3.1.0 Available
nrf v3.0.2 Available
nrf v3.0.1 Available
nrf v3.0.0 Available