Is there a way how to save team subsite as a template? Because theres no "save site as template" action available.
Although it might be possible to save a modern (sub) site as a template using classic features, is not supported. See this thread: https://techcommunity.microsoft.com/t5/SharePoint/Save-Modern-Team-Site-as-a-template-amp-provision-using-Classic/td-p/95307
If you want to use a site as a template, check out the PnP Provisioning Powershell cmdlets. Here's a good blog post describing the process for a classic publishing site. http://sharepoint.handsontek.net/2017/10/29/save-publishing-site-as-template-the-right-way-using-pnp-provisioning/
Saving site as a template is not supported on "modern" team site. Also not supported for sub sites in site collections which root site is a group associated team site or communication site.
Refer to the section what's not supported on "modern" team sites:
Within SharePoint Online, they have recently introduced the site template concept called Modern Site Designs. With Modern Site Designs, you essentially have the ability to use them in two ways:
Both of these ways are great resources for enforcing governance across your sites and for reducing the amount of time needed for the initial setup.