I have a similar problem with a few differences as described with the original poster on this old thread.

My flooring is Cali Bamboo Geowood flooring (from the manufacturer's website: GeoWood is an engineered hardwood combining real timber layered over GeoCore -- Cali’s stabilizing limestone composite foundation. This technological breakthrough yields rock solid hardwood flooring with exceptional AquaDefy water resistance and comes at a lower price point than solid wood planks.) In reality, the geocore backing feels more like a vinyl plank.

Under this floating flooring is Roberts AirGuard 2mm thick 5-in-1 Underlayment with Microban. The underlayment is sitting on Advantech subflooring.

At one spot on the floor where two planks meet, these two planks and an adjacent plank have some play which often causes a creaking noise when someone steps on that spot. I can feel play in this 3" x 3" area when I press the floor with my hands. Rest of the floor is solid with no play.

Questions:

Since there is AirGuard underlayment under the floating floor, would injecting an adhesive to fill the void in this area of the flooring create any issues? When drilling a hole for injecting the adhesive, I'll be careful to not drill through the underlayment. If I'm successful, the three planks would be adhered to each other, but this won't glue the floating floor to the subfloor. It would technically still be floating. Any thoughts?

Should I use a water based adhesive like Titebond or a polyurethane adhesive such as PL Premium?

You could glue everything together. I would recommend epoxy glue that will harden without needing dry. It hardens with a chemical reaction over a certain amount of time. If any gets on the surface when injecting into a small hole, you can use vinegar to clean up the surface.
3M makes an injecting system that supplies a small drill, an epoxy/ hardener kit and the injector gun. Not cheap, but works the best.

Thanks Pete. Is this the 3M kit you mentioned - 3M Epoxy Hardwood Repair Kit? Do I need the 3M Epoxy Dispenser to use the repair kit?

Yes, the dispenser is like a caulking gun and when you press on the cartridge it mixes and presses the epoxy into the hole you have made with the drill.