Rear Derailleur wire sags completely in higher gears
What you describe suggests friction in the rear housing loop. It fits with the problem getting progressively worse, and with the apparently slack cable, presumably along the downtube or chainstay. This can happen from corrosion, contamination, kinks in the cable/housing, or the housing or cable fraying or coming apart.
It might need new cable and housing. That is normal maintenance and not a big deal if so.
Put the shifter in 7 and leave it there. Pedal with one hand while pushing the derailler inward up to the big cog with the other. Use the slack you've created in the cable to slip the rear loop out of its stop. Try to slip it up and down the cable to inspect for friction. Inspect it for the above. If it's dirty or corroded, get it clean. Put a few drops of oil along it. Shove the derailleur inward again as you reseat the housing in the stop. See if there's any improvement. It would be normal to need to readjust the tension at this point.
If the bike has a housing segment near the seat cluster, it could also be the source of the problem.