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@thrijith I took the liberty to make some changes directly so you can better see the direction I think this should take. Let me know what you think.

I also saw that we still have many areas where video/mp4 is hardcoded. For example in our custom video block edit component.

I took the liberty to make some changes directly so you can better see the direction I think this should take. Let me know what you think.

Thanks @swissspidy 🙂, I was not sure, how to go about adding changes needed for store.

I also saw that we still have many areas where video/mp4 is hardcoded. For example in our custom video block edit component.

Are you referring the accept part?

It doesn't allow selection for other extensions when using Upload button in the Video block.

index 412fabac..d45a5580 100644
--- a/assets/src/stories-editor/components/custom-video-block-edit.js
+++ b/assets/src/stories-editor/components/custom-video-block-edit.js
@@ -235,7 +235,7 @@ class CustomVideoBlockEdit extends Component {
 					className={ className }
 					onSelect={ onSelectVideo }
 					onSelectURL={ this.onSelectURL }
-					accept="video/mp4"
+					accept={ allowedVideoMimeTypes.join( ',' ) }
 					allowedTypes={ allowedVideoMimeTypes }
 					value={ this.props.attributes }
 					notices={ noticeUI }
diff --git a/assets/src/stories-editor/components/with-enforced-video-upload-type.js b/assets/src/stories-editor/components/with-enforced-video-upload-type.js
index 39c49239..7520580c 100644
--- a/assets/src/stories-editor/components/with-enforced-video-upload-type.js
+++ b/assets/src/stories-editor/components/with-enforced-video-upload-type.js
@@ -14,11 +14,11 @@ import PropTypes from 'prop-types';
  */
 export default ( InitialMediaPlaceholder ) => {
 	const withEnforcedVideoUploadType = ( props ) => {
-		const { accept, className } = props;
+		const { accept, className, allowedTypes } = props;
 		let newProps = { ...props };
 
 		if ( 'wp-block-video' === className && 'video/*' === accept ) {
-			newProps = { ...props, accept: 'video/mp4' };
+			newProps = { ...props, accept: allowedTypes.join( ',' ) };
 		}
 
 		return <InitialMediaPlaceholder { ...newProps } />;
@@ -27,6 +27,7 @@ export default ( InitialMediaPlaceholder ) => {
 	withEnforcedVideoUploadType.propTypes = {
 		accept: PropTypes.string,
 		className: PropTypes.string,
+		allowedTypes: PropTypes.arrayOf( PropTypes.string ).isRequired,
 	};
 
 	return withEnforcedVideoUploadType;

Since allowed video type is available in props, we could do something like this to remove usage of hardcoded mime type from custom video block element.

with-enforced-video-upload-type.js is probably going away soon as we don't really need that anymore now that we have custom-video-block-edit.js - see #3189.

Otherwise your suggested change looks good 👍

I have updated the accept attribute value for custom video edit block, I think the PR can be merged, as it allows selection of other mime type in Background Media as well as video block. Please let me know if it needs any other change.