I used to be able to create my own embeds with regex etc but I can't seem to find the option anymore in the ACP.

I was looking to create an auto-embed for Apple Music links as described here: https://tools.applemusic.com/en-gb

Is this no longer possible?

I'm assuming you recently upgraded from 3.4.x to 4.4.x and I ran into the same issue as you with Apple Music.

Unfortunately, Apple doesn't support the oEmbed standard, so it's not easy to add their embeds. However, I have had success with BandCamp (who also doesn't support oEmbed) by creating a custom button in the Editor so people can paste in the BandCamp ID and the button does the rest of the IFRAME embed process.

Not as easy as copying a URL, but it works.

Now, if the provider you're wanting to create an embed for DOES support the oEmbed standard, then you can add it via a plugin - I use @Nathan Explosion excellent (NE) oembedServices management addon and it works great:

 

Thanks for the info but my members will have to deal with it not embedding - it's a shame the functionality was removed from 3.4 as I had several embeds I made myself that now no longer work.

The interface was removed unfortunately. A custom plugin can still hook into the editor and create any auto-embedding you want.