As per Microsoft supported option, you can follow below article and use site definitions instead of site template.
"saving publishing enabled sites as a template is not supported and it does not work. You cannot use this option to create new sites. Instead you should create site definitions (..\web server extensions\12\template\SiteTemplates) and provision ...
You can only create site templates from classic sites or modern team sites not connected to a Group.
1.Disable publishing features.
2.Allow custom scripts.
Template Type ID for Promoted Links List is 170
You can try below list instance code in Visual Studio with SharePoint feature to create a new Promoted links list:
Follow below steps:
Create new empty element in Visual Studio solution.
In its element.xml file, copy paste below XML code.
Deploy the solution in SharePoint farm.
In SharePoint site, you will ...
It can be done, but you need to download the site template as a solution file and then re-upload it to the solution gallery every time you create a new site.
Here is the full answer:
Create site collection using custom site template SharePoint Online
To Create a SharePoint site collection based on a custom site template in SharePoint Online / Office 365
Save your site as a template
Note: Only team sites can be used to create a site template, please see this article for more information:
Download the site template ...