Brake levers for riding in upright position
There are two sorts of brake lever that would suit this description - given mention an older ten speed you're probably remembering these:

Sometimes called Suicide Brakes, or secondary levers/safety levers or something similar.  They're not common any more because the braking effect is low, probably for mechanical advantage reasons.
Not recommended unless you're going for original-look.  I have one on my 80s bike and its just for show - I never use it.


The more-modern version is a Cyclocross interruptor brake lever like these.  Functionally they're similar, but pull the inner separately to the outer, they don't pull the existing brake lever for you.
These brake levers work fine, and function either in concert with dropbar brake/shifters  as pictured, or can be used as brake levers by themselves if you're on a flatbar bike.
Again, these are mostly cable-brake based, but there are also hydraulic versions of the interruptor brake.  Shimano's GRX groupset has them as an option.

Given you're looking for a new bike, this doesn't fit your need, but...
The third option is to either learn to brake with existing drop bar brakes, or look at upgrading to more modern brifters.  The difference there is that the whole hand position has improved over time, and now braking from the hoods position works much better than older dropbar brakes.
Compare these with the first photo and you can see how different the angles are.

See also Braking on a vintage road bike