Is it possible to use the salesforce identity licence to login to another service online?

Yes, using a salesforce identity license is possible.

For every experience cloud site you use, it can act as an IDP. This includes external users linked to the site. Here are the steps to enable communities as IDP, note it is very similar to the regular salesforce as IDP. Create my domain for your organisation. It is under the Domain Management in setting up nder Security, control find Identify Provider tab and click "Enable Identity Provider" for the org. Create a connected app with the "Enable SAML" checkbox checked. Provide below parameters from your Service Provider Assign Profiles for the connected app Download metadata for communities. Under SAML Login Information, click on Download Metadata. Note there will be a section called "For Communities". The metadata has the certificate that you can share with your Service Provider