I don't have a picture (I can grab get one if you like), but I did the same thing in my current project - new wood floor in the kitchen going right into existing in the dining room. The floor installer feathered some of the new boards into the dining room floor so it looked continuous, then I had all the existing floors sanded and refinished and stained the old+new 1 color. The result is a transition that looks completely continuous and uniform. Of course I had to refinish all my existing floors to do it. If you don't want to do that the only thing I can imagine working is a perpendicular strip to edge the new and old. It'd be impossible to match the old stain with new perfectly so you'd need something to separate the two. I have a spot in my house where the boards are mismatched so whomever installed it back in the day put a strip. I attached a picture of that.

G&S said it all except to be sure that the adhesive didn't etch the surface. If it did there will still be marks after the adhesive is removed. That said, you can try mineral spirits first without harming the finish (assuming it's urethane finish). If a customer calls me and says there's glue on the floor I send someone out to clean it.

Those "gaps" are mild. They are normal. They are expected. They tell the story that they are original. They are meant to be there. The new floors will eventually do that too...which means they will match (eventually). It might take a decade...but it will happen. And don't forget that once everything is sanded down, you will be VERY surprised at how those "gaps" seem to go away (visually). Why, you ask? Because some of that is dirt. Once the floor has been sanded down (1-2mm of wood is taken off with the sanding), the dark material between the planks gets shaved off as well. And voila...they look cleaner (because they are). Relax about the absolutely normal spacing between planks. Unless you have museum quality climate control, this LITTLE bit of shrinkage is normal and to be expected with every floor (especially if it is 30 years old).

I am thinking about using a shellac finish and sealer on this hardwood, which will be the floor for a kid's room. This Bullseye traditional finish and sealer product from Zinsser seems widely used and well liked: https://www.lowes.com/pd/Zinsser-Bulls-Eye-Clear-Shellac-Actual-Net-Contents-32-fl-oz/3449840 This particular product says it is clear, and I think there is an amber tinted version. Can shellac be applied without problems to hardwood? I believe I could put poly on top of the shellac and be done. Is this right? Any tips or warnings? There is also this Sealcoat by Zinsser, which does not appear to be shellac based. https://www.amazon.com/Rust-Oleum-Zinsser-854-Sealcoat-Universal/dp/B000C02BXW/ref=sr_1_3_mod_primary_new?dchild=1&keywords=zinsser+shellac+sealer&qid=1610393849&sbo=RZvfv%2F%2FHxDF%2BO5021pAnSA%3D%3D&sr=8-3 Would the Sealcoat be a better option to just put over the hardwood? I have read elsewhere that shellac can be applied over poly, which is good since I don't know what is on the existing floor. Other places say shellac could be sanded after application, so when we have a chance to completely sand and refinish this floor, I would probably want to do this. Does this sound like an acceptable temporary fix, or is there something I should consider before proceeding? Would shellac ruin or damage the hardwood. I am also thinking about LVP, but I am concerned this hardwood floor is not flat enough for that. I understand the subfloor for LVP must be 3/16" within about a 1 foot diameter to work. Any ideas about this? Is there a way eyeball this floor to determine whether click LVP could be put down? Thanks!