Best is to route the earthing wire directly as short as practicable with minimal bends and separated from anything else that might be an alternate (even though less conductive) path to earth.
Any bonding of a lightning ground earthing electrode to Ufer ground means the lightning electrode is an expansion of the building's single point earth ground.
For example, this application note shows how single point grounds for separate structures are also interconnected via a buried wire:
Is that too much complexity for the actual risk? That decision is the art - how much risk is a building at? How much protection is really required? Telcos do this layering of earth ground; each protection layer is defined each earth ground. But then 99.5% protection is insufficient for telcos. So they spend more on earthing.
Another and maybe simpler solution is to connect each air terminal earthing electrode (also by buried bare copper wire) to a nearest point on the Ufer ground loop. This still creates equipotential. Not as good as in the previous paragraph. But typically would be more than sufficient.
However most do not even do that much. Most only install air terminals to an earthing electrode (outside of the Ufer ground loop) and let earth conductivity be sufficient to make a conductive connection between the two earthing systems.
Ufer ground creates a loop so that anything inside the loop is at equipotential. As long as the air terminals are earthed outside that loop, then building equipotential is not violated. Each above suggestion is how to make that internal equipotential better; more robust. How much need you do? That judgment call is best determined by conductivity of geology (also taking into account any variations in soil on different sides of the building created by soil of conductive pipes/wires in that soil), history of surges over the past decade, and how necessary that protection is. Remember numbers from the IEEE citation. We are discussing protection where all solutions well exceed 95% effective. So it is really more about what is practicable verses how much protection is really required.
Now, let's say the air terminal is grounded by a separate earthing electrode. So, where are earthborne charges that a cloud is connecting to? If an earth conductive path goes away from the building, then a connection to Ufer ground increases conductivity and does little for increasing or decreasing equipotential. However if those earthborne charges are beyond the building, then the Ufer ground must conduct earthborne lightning currents around the building. Any weakness in that conductive loop (and no loop is perfect) means less equipotential inside the Ufer ground. Installing an air terminal ground loop outside the Ufer ground means less current flows through the Ufer ground; means the building inside that Ufer ground has even better equipotential. This paragraph to better explain how the direction of earthborne currents is relevant to why the same earthing system can be better or worse. This paragraph also explains why other geological features (ie nearby buried transcontinental pipeline) can change the behavior of an earthing system by changing the direction of earthborne surge currents.
BTW, research also says blunt air terminals are more effective than pointy ones. Research that contradicts popular beliefs.
BTW, some put a wire net to eliminate cracks in a poured concrete basement floor. Integrating a concrete floor into the Ufer ground is another trick to create both better conductivity and equipotential beneath the entire building.
BTW, better bonding of Ufer ground rebar involves cadwelding so that bonding is not degraded by large currents. If using some cadwelding, cadweld rebar closest to the single point ground connection - where most surge currents may be conducted.
Again, the art is to decide how much protection is required. Earthing mostly defines protection. To better appreciate this art (if possible), learn more from what telcos or other nearby high reliability facilities have done.