We want to convert two rooms that have carpeting (over concrete) to hardwood flooring, but they both need to flow relatively seamlessly with an adjacent hardwood hallway that is on tar and screeds. Since the carpeting and padding is on concrete, what sort of hardwood flooring should we be looking at for the two carpeted rooms to keep all the floors as seamless as possible?

We'll need to know more such as the height of the older flooring. Tar and screeds sound like 1 1/2 inches high then 3/4 inch hardwood?

What is the height difference between the existing floor and the concrete? Was the old carpet at the same level as the existing floors?

Seamless is always nice to have, but you might end up sacrificing quality to achieve it.

You might consider removing the hallway floor and create a transition where the hallway connects with the rest of the house. You may only need a 5/16" reducer to tie the two areas together depending on the layout.

Much more information would be needed.

The older hardwood floor is 3/4" hardwood and the concrete under the carpets are even with the base of those 3/4" hardwood planks. I can't see the tar and screeds so I can't tell for sure how deep they are.

The easiest floor solution would be to "float a 5/8th inch thick engineered floor over the concrete, after you have flattened the slab.
Install a moisture barrier and an eighth inch foam pad, for comfort and to take up some unevenness. Both characteristics can come from a pad that has a moisture barrier in the backing. Read all the directions for installation before you start.
Any questions can be answered from the supplier.
If you are just a little low in elevation you can add some tarpaper to shim it up near the door. You will need to use a T-molding that is fastened to the old flooring
so you can get the proper expansion gap for the floating floor and new base boards or remove the old ones and install after the floor to cover the expansion gap at the edges.