Many thanks @quicksketch - I've tested this PR and can confirm it works with CKEditor 5.
The icon and file link are in separate <p> tags but I can live with that - a little css sorts it out. This is the code that was added to the body for me:

<p>
  <img class="file-icon" src="/core/modules/file/icons/application-pdf.png" alt="" title="application/pdf">
</p>
<p>
  <a href="/files/members/Face_masks_order_form_2020.pdf" title="Face masks order form 2020"><span class="file">Face masks order form 2020</span></a>
</p>

@nattywebdev Thanks for testing! Do you mean that every time you insert a file, it creates a new paragraph tag? It should respect where the cursor is in the document, but I admit I did not test that level. It's entirely likely the the code I used will always wrap the newly inserted content in <p>.

Revisiting this after the break and I find that the additional

tags are now not inserted in my example. No idea what caused that issue before but my current example works just fine:

<p><span class="file"><img alt="" class="file-icon" src="/core/modules/file/icons/application-pdf.png" title="application/pdf"> <a href="/files/docs/Test_Document_1.pdf" title="Test document" class="ext" target="_blank">Test document</a></span> </p>

So thank you @quicksketch !

That's great, thank you @nattywebdev. However, now that backdrop/backdrop-issues#6770 has been released in 1.29.3, we can improve this code to use the new variable provided by CKEditor 5 core, so we don't have to track the instance ourselves. This can be merged as-is, but it could be improved by now removing the manual tracking.

@quicksketch is this now dealt with by backdrop/backdrop-issues#6770 ? Or is something needed in the Insert module to access the relevant variable? I have no clue how to do that so will need help.