The play in question: https://norig.myfootballnow.com/watch/899#161297

What happened: the ball carrier is tackled at the defending team's 20 yard line, and the tackling defender is charged with a facemask penalty for 15 yards. The next play starts at the defending team's 5 yard line.

What should have happened: the ball carrier is tackled at the defending team's 20 yard line, and the tackling defender is charged with a facemask penalty for 10 yards -- half the distance to the goal line. The next play starts at the defending team's 10 yard line.

From the NFL officiating rules https://operations.nfl.com/media/4693/2020-nfl-rulebook.pdf Rule 14 Section 2 Article 1, enforcement of penalties that would result in the ball moving closer to the goal than half the distance to the goal line, the ball should be placed at the half-distance mark. Rule 8 Section 6 Article 1(c) also dictates that enforcement of the penalty should be from the spot of the foul (which is correctly done here).

Where on the field does the penalty change from 15 yards to half the distance. The foul seems to occur just before the 20, as shown by the spot following the penalty (approx. 5.25 yards from the goal line)

If the rule changes beyond the 20yard line to 15 yards then the SIM is correct. If half distance is in play until the 30 yard line, then your correct it should be from 10 and one eighth of a yard to go

It's always half the distance if the yardage is more than half of the remaining field.

A 5 yard penalty inside the 10 yard line is half the distance.

A 10 yard penalty inside the 20 yard line is half the distance.

A 15 yard penalty inside the 30 yard line is half the distance.

The way it's written in the NFL officiating rulebook is that when a penalty enforcement would put the ball closer than half the distance to the goal, the ball penalty is enforced half the distance. The only exceptions to this rule are certain spot fouls, such as defensive pass interference.

It is not uncommon that sometimes judges make rash decisions and do not notice some details of the violation. Still, they are guided based on what is happening on the field, and we only see a record on the screen that can search for the situation.
When I read the rules, I wondered how much distance I had to overcome. It turned out that https://parentportfolio.com/how-big-is-an-acre/ a standard acre is 4,840 square yards[/url]. It turns out that you do not need to cross such a large part of the field.
By the way, can I find out why you are analyzing this particular situation? Even in soccer, fans rarely remember any refereeing decisions and analyze them.