How to make "Swing" or "Straight" tempo marks visible to the reader?

I added “swing” and “straight” tempo marks which I can see in signposts and they affect playback, but they aren’t being rendered in the score, or have any properties that I can turn on.
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I thought about creating another custom tempo mark just for the written indication, but it has few obvious disadvantage in that 1. it would override the tempo, which I’ll have to manually set to be the same thing as before (which will make it harder to change) and 2. if I decide to change the swing/straight marks I need to change two things.

Is there a better way of doing it that I’m missing?

Dorico doesn’t (yet) have visible swing markings, so for the time being you will probably want to add some system-attached text, perhaps using Metrico.

Can I ensure that system attached text will always be at the top staff of any layout? Like tempo marks are

Yes. The clue is in the name. System objects appear above the top staff (and any other staff you have nominated in Layout options>Staves and systems>System objects)