I have been given conflicting advice on how to plant geraniums and other (what are here) annuals.
One person said to really tease out the roots so that they don't form a root ball. Another said that you absolutely shouldn't do that because the plant is already in a state of shock from being transplanted in the first place and that disturbing the roots will cause further unwanted suffering

Over the two years that I have planted geraniums there have been too many other variables to discern whether or not teasing or not teasing out the roots is more beneficial for the plants. I want what's best for them.

Any advice gratefully received

The suggestion I gave in answering your query about cutting ack or not, I suggested at that time to examine the roots and clean them up if they showed any sign of damage. That says if you see any blackness, or detect any smell from the roots, they should be cleaned of any and all soil. That soil is dead...there's no need to carry that forward.
There's no need to wash the roots, just use your fingers to knock off the soil.

The new plantings will have fresh, new potting soil where no fertilizer is needed.
The new plantings should have a clean pot with drainage holes to which after watering, the pot drains well.

Roots of the old, tired out plants are not so tender you cant inspect them, handle them and clean them up.
By all means, tease them out....let each piece of root enjoy the new soil they're going into.