Does the Media Module Support SVG Images?

For uploading .svg image you need to install svg_insert and svg_image module.
Please check the link for these modules:-
https://github.com/58bits/insert_svg
https://www.drupal.org/project/svg_image

## Installation
1. Download and enable the module as usual.
2. Go to your filters admin (admin/config/content/formats).
3. Edit the format on which you want to enable the insertion of SVGs.
4. Drag the 'S' icon to the "Active toolbar".
5. Configure the plugin settings in the vertical tabs above the toolbar
Save.

I've installed the svg_image module, but it doesn't seem to function correctly with media.

#3060504: Media Library widget does not render svg images

At this point, there are several contrib modules that provide SVG capabilities, so it is hard to know what combination of them works. Below is my preferred recipe, but 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

This is my recipe that works with Media in Core, and leverages SVG Image Field (copied from https://drupal.stackexchange.com/a/280836/3167)

1. Enable Media module and the experimental Media Library module both of which are found in Drupal >=8.7 core.
2. Download and enable SVG Image Field and apply to it the patch from #3053011: Support Media Library.
3. Go to /admin/structure/media and click the "Add Media Type" button.
4. For the Media Type Name specify 'SVG'.
5. For the Media source select SVG from the dropdown.
6. In the field mappings map Name to Name (the only option in the dropdown).
7. 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.
8. 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).
9. Go create a node, and click the "Add media" link.
10. Notice that the Media Library loads with a vertical tab for each kind of media type bundle you enabled in step 8 on your node configuration screen.

There is a contrib module to help with svg images, a new release today.
https://www.drupal.org/project/svg_image

The Media module itself has no opinion about SVG images. The Image module, on the other hand, doesn't normally allow SVG to be uploaded into any image field, due to the various security and integration issues (i.e., image styles). This is the case regardless of whether the media system is in use.

The SVG Image module does seem to be a good solution here. Getting SVG support into core's image system would be outside the scope of the Media module right now.

I think that, given all these things (and the fact that other issues exist to add SVG support to core), I'm closing this as "works as designed".