Remove "frontend_only" badge, or make it so we can disable them separately

### Is there an existing issue for this?

- [x] I have searched the existing issues and checked the recent builds/commits

### What problem are you experiencing?

Please make the "frontend_only" badge disappear. It clutters the UI unnecessarily.

In the settings there's a drop down called "Node source badge mode" that let's us:
None
Show All
Hide built-in

Only "None" hides the frontend badges.

### When does this problem occur?

Only "None" hides them currently.

### How often do you encounter this problem?

Multiple times per day

### How much does this problem affect your workflow?

Causes moderate inconvenience

### Current workarounds

Moderate is too low, but it doesn't stop me from working. It's a major annoyance!!!

### Ideas for solutions (Optional)

Please either add an option there, or better yet, add it's own option to hide them, as some users might want one of the existing options and to make options that cover all scenarios would be over kill.

i.e.:
None
Show All
Hide built-in
Hide built-in but show frontend_only
Hide frontend_only, but show built-in
Show non built-in, but hide frontend_only

Or make them frontend_only invisible again!

### Additional context

_No response_

┆Issue is synchronized with this [Notion page](https://www.notion.so/Issue-7618-Remove-frontend_only-badge-or-make-it-so-we-can-disable-them-separately-2cd6d73d3650810fa5b7c66be78b2eeb) by [Unito](https://www.unito.io)