Site Editing: stay in Template Editing mode after applying changes

[annezazu]

Describe the bug

Right now, after entering template editing mode and saving changes, you're brought back immediately to the original post/page you were working on rather than remaining in editing mode. Assuming we make it easier to switch back and forth
per #27899 it would be great to stay in each mode after applying changes rather than being dumped back out of it.

To reproduce
Steps to reproduce the behavior:

1. Install Gutenberg 9.6+ and a FSE ready theme.
2. Go to Posts > Add New
3. Make some changes to the post > Publish or Save Draft
4. Use the option to edit the template to switch into template editing mode in the document settings section.
5. Make some changes to the header, footer, and post content.
6. Select "Apply" and save all changes.
7. You'll then be brought back to the post editor rather than remaining in template editing mode.

Expected behavior

I expected to apply changes and remain in template editing.

Screenshots

Here's a video where I talk through this: https://cloudup.com/cerjgGlXiLv

Editor version (please complete the following information):

• WordPress version: 5.6
• Does the website has Gutenberg plugin installed, or is it using the block editor that comes by default? Gutenberg
• If the Gutenberg plugin is installed, which version is it? 9.6.2

Desktop (please complete the following information):

• OS: MacOS
• Browser: Chrome
• Version:87.0.4280.88

[annezazu]

Just tested this with Gutenberg 11.0.0 and WordPress 5.7.2. Closing out as it now leaves you in template editing mode after saving :)