Tag autocompletion inside of template does not seem right (different from regular HTML files)

[basuneko]

• I have searched through existing issues
• I have read through docs
• I have read FAQ

Info

• Platform: MacOS
• Vetur version: v0.26.1
• VS Code version: 1.47.3
• VSCode settings have been completely reset
• No other extensions installed

Problem

Hi. The title might be a bit confusing, apologies for that.

When I type out a new opening tag, I expect a matching closing tag to be added. This does not happen.

In addition, when adding a tag inside of a tag of the same name (i.e. div inside of div), the only suggestion provided converts my new tag into a closing tag for the parent and I end up with

<div>
</div>
</div>

instead of

<div>
  <div></div>
</div>

So far I've tried setting html formatter to none but that had no affect. I couldn't find any other relevant options.
Editing regular html files works quite differently - gif below.

Reproducible Case

Case 1

1. Inside of the template, type <div
2. Type the >

Expected: it should create <div></div> and put the cursor between the tags
Actual: suggestions disappear and nothing happens

Case 2: Nested divs

1. Create a div and put the cursor inside of it:
2. Add a new opening <div>

Expected: The top suggestion should be to create a new <div></div> pair
Actual: The only suggestion is to close the parent tag. Need to press escape to dismiss suggestions.

For comparison, this is how it works in an html file:

[octref]

Part of #565.