Lots of good suggestions here!
The "botanical edging" sounds like a great idea. If you had some slope right at the edges of the bed, it would even convey at least a LITTLE surface runoff water around the bed to the lowest spot.
You can prevent a lot of water from running downhill INTO the bed with a deeper trench up-slope from the bed, leading runoff away ... to some other low spot. If you have a low spot.
If you had a spot in your yard LOWER than the bottom of the new bed, you could make a French drain from the bed down to that spot ... but it sounds like that isn't an option. That's the only way I know to give a below-grade bed a non-flooding root zone.
If the soil in that bed is any kind of decent soil, it might be a recoverable investment, if you throw more money at it, or if the company that cheated or sabotaged your yard will make it good (so you don't sue them?)
Maybe they would dig that bed out again, and move the good soil to where it SHOULD have been for a RAISED bed - namely raised ABOVE grade. They might only pile it up, and leave it to you to add raised-bed-walls (wood, cinder block, paving stones on end, pretty boulders).
Maybe let them back-fill the hole with "whatever".
If they did that, they could then move the good soil back on top of "whatever" and your raised bed would be where you originally planned it.
Or line it with plastic and have a "water feature". (You would need to add water during dry spells. )
The company that dug your bed DOWN into non-draining clay should be shot, or at least forbidden to call themselves landscapers. Even if you "seldom" have heavy rain, a bed that drowns every plant "occasionally" is no bed.
I think the most extreme form of re-engineering the yard, (other than totally re-grading everything which would ruin lawns and even some trees, and might not even be possible), would be to dig down wherever the current lowest spot is, make a deep hole there, like a mini-well, and backfill with gravel. Yup, a full-blown French drain. And then trench other beds down TO that new low spot. If its bottom happens to have at least a little "perk", that would help.
