Which will be a better approach to display this banner on a dashboard?
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It really depends on the context the banner is placed. When there is a clear difference between context and banner, i would go with option 2.
In option 2 you distinguish between information and action. That makes it more clear for the user. First you get the information and can then express an action. I would also would place the more important button (in my view, Exercise new) on the right side. So the user can scan which option he wants to use (like: no, yes).
Option 1 has more noise, and it's harder for the user to scan what is information and what are his possible interactions.
If you go on mobile, the actions would be right to place them under the Information, but with a little more space to make it more clear that you have the information and then actions.
Hard to say. Do you have the option to A/B test or even eye-track?
Intuitively (which you should always take with a grain of salt):
Exercise nowis your primary button / Call To Action on the whole site, I think you would benefit by making it bigger and more outstanding (more padding, maybe a subtle gradient, border or shadow...), so that you definitely see it as a user - don't underestimate how easy it is to overlook things when in scanning mode...