Update!
Friday afternoon the person who been the building inspector for my town for decades came to my house to take a look.
He thought it was strange. Said that normally there would have been a wall going from the edge of the garage floor to underneath the top stair. That leaves just air behind the stairs. In this case he hypothesized that they did not do that but, instead, used fill behind the stairs. Would have to remove a stair to verify.
Initially he stated that the most simple solution would be to cover up with a board the area where the sand was coming in. Then he noticed that the sand was also coming on to the basement floor through the bottom of the board that is adjoining the doorway in the basement. So that first solution would only take care of half for the two problems.
An hour after he left another friend came by who'd been a carpenter and who'd done a lot of work on my house (vinyl siding, installing two garage doors, redoing bathroom). He thought we should remove a stair to look and to remove the board in the basement adjoining the doorway.
He said to text him Monday morning about getting this all done on Monday.
Yesterday I asked the person who does my snow plowing but who is also a practicing carpenter. Two years ago he did extensive work enlarging my garage door opening and installed the side garage door.
Using his crow bar and a hammer he somewhat pulled out away the lower third of that basement board. Enough for use to hold on to the board to pull it away enough to look inside. He ascertained that there is nothing coming from the right side of the cavity.
Note I am defining the cavity as the area that is enclosed by the board in the basement and the board adjacent to the top of the right stair.
He suggested that my friend cut off the bottom of the board so as to get in the area and then just nail it back when done. Advised using mortar to seal up the space where the sand / dirt is coming in (top of bottom stair on the right).
Note that way above I'd stated how I'd filled a bin with over a cubic foot of sand / dirt. Before he came to my house I saw that the area near my two garage doors was like an ice-skating rink. I myself slipped when trying to chip it with a shovel. I was about to go inside the house to get kitty litter to put on the area leading to the small garage door when I saw that bin of dirt / sand. Used it to cover the skating rink ice in front of that door!
So that is where things now stand with more current pictures below.
Finally is that after today I cleared out all the standing sand / dirt on the bottom step and in the basement I'm not seeing any more movement. Therefore, still don't know what caused this for an 80-year-old house but it seems fairly minor. It may have stopped and does not need the mortar but having gone this far ...why not do the mortar.

Above provided by: Vinny, who always says: "I only regret that I have but one lap to give to my cats." AND "I'm a more-is-more person."