I think playing an Action during your buy phase like this is OK. Certainly preferable to warping back to the Action phase temporarily. Unless there's some broken interaction that I'm missing.
Well, most actions wouldn't work the way is intuitive. Since you've already bought a card, you couldn't play any more treasures if you drew them with that action you played. And unless you had some source of +Buy, you wouldn't be able to buy anything new if you played something for coins because you've already bought a card. Nearly all actions played during the buy phase after you've already bought a card are actually useless - it would be a very niche ability, useful only for a few weird combos, and just sitting there tripping people up in all the other cases.
I was envisioning going back to the action phase, starting with 1 action, and then continuing on to a new buy phase as normal, etc. Dunno, It just seems like "play an action card during your buy phase" gives rise to lots of weird unintuitive cases that don't work the way people would think, whereas "go back to your action phase and then continue as normal" would work pretty much as intended.
Though perhaps both of these are too far out, and we'll get far simpler things than that. After all, instead of "play an action" the card could just have an on-buy ability which is equivalent to something typically found on an action.