Please refer to the following documentation for more details into this: https://support.atlassian.com/jira-cloud-administration/docs/convert-a-project-to-a-different-template-or-type/
Basically you need to create a new project and bulk move issues into the new project.
As mentioned above, that would be the solution but to be honest the template really only helps you in the beginning but it does not restrict what you can do in a project.
For example, one template may start you off with a specific set of issue types and request types and another template will start you off with a different set. No matter the template, you can remove everything it added and add whatever you want to it.
If you have a ton of issues in a project already, I wouldnt recommend making a new project just to change the template.
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