Media Module: How to enable SVG files
You can use SVG Image Field module with Drupal 8 and the new core Media module.


Enable Media module and the experimental Media Library module both of which are found in Drupal >=8.7 core. 
Download and enable SVG Image Field and apply to it the patch from Issue #3053011.
Go to /admin/structure/media  and click the "Add Media Type" button.
For the Media Type Name specify 'SVG'.
For the Media source select SVG from the dropdown.
In the field mappings map Name to Name (the only option in the dropdown). 
Click save. Then proceed to configure the Form Display and the Display for the Default and Media Library view mode at /admin/structure/media/manage/svg/form-display and /admin/structure/media/manage/svg/display respectively. You'll most likely want to just enable the "SVG" field, and disable the rest of the fields. The default display you can choose to use an inline SVG option.
Add a Media reference (Entity reference) field to your node types and configure it to allow the SVG bundle type.  Optionally, enable other bundle types as well, like Image if you want to allow both images and SVGs in the same slot).
Go create a node,  and click the "Add media" link.
Notice that the Media Library loads with a vertical tab for each kind of media type bundle you enabled in step 7 on your node configuration screen.




If you're still on the fence about how to choose the right SVG media module from Drupal 8 contrib, you may find my comparison of the 3 modules helpful to guide your decision making:

https://drupal.stackexchange.com/a/280837/3167