[M T]

Top of the seventh, two outs, two strikes on the batter. Umpire decides that the batter was hit by a pitch. Watching slow motion replays for I don’t know how many times it looks to me like it hit the bat.

The ump has one thing we don't: sound.  The ump signals the ball struck her left forearm.  It couldn't hit there, but one question is, did it FIRST strike her left fingers while on the bat or did it first strike the base of the bat.
I don't know if a struck-by-pitch is reviewable, but I'm glad Stanford didn't ask for a review.  The video isn't clear on what it hit.

At 70mph, the ball travels 3.4 feet every 30th of a second.  I think this is the best view you'll get

I see a bit of the bat between the ball and the left hand. Whether  the ball is not yet to the bat or is already past the base of the bat seems impossible to know, or if the ball has already bounced off the base of the bat is likewise impossible to know.

To my mind, the movement of the bat that I see in the slow motion view from behind the pitcher makes me think it hit the bat.  But that is only an impression.

So, while I disagree with the call, the call would not be overturned.

There are details in the rules about where the ball and the batter are (presumably at the time of contact), For this pitch in the 7th inning, the ball appeared to be entirely in the batter's box (hence 11.13.1 applies)

However, for the 1st inning call where the Stanford batter was hit by a (called) ball that was not entirely in the batter's box, so 11.13.2 applies, Appendix A "Feet and Lines Chart" indicates "Batter at bat/ball contact" has a Permissible Position "within" (vs "in/on") the "batter's box". By the definition and the overhead view, she was within the batter's box. She did (and announcer agreed) make a move to avoid being hit. So, did the umpire make the right call?

The rule says "any part of the batter or their clothing while THEY are in the batter's box". It s not "while the batter is in the batter's box" but "any [touched] part of the batter is in the batter's box". Note that any of the touched part has to be in the batter's box, not all. The overhead view supports that the part of the ball furtherest from the plate (a part that did touch her) is outside the (outer line of) the batter's box. So, I think that call was correct also.

11.13.1 A batter is awarded first base when a pitch, neither swung at nor called a
strike, is entirely within the batter’s box and it strikes the batter or their clothing.
No attempt to avoid being hit by the pitch is required; however, the batter may
not obviously try to get hit by the pitch. (See Rule 11.13.3.1.)
11.13.2 A batter is awarded first base when a pitch neither swung at nor called
a strike touches any part of the batter or their clothing while they are in the
batter’s box, except as noted in Rule 11.13.3 that follows.
11.13.3 The hit batter shall not be awarded first base under the following
circumstances:
11.13.3.1 The batter made no attempt to avoid the pitch (which is not
entirely in the batter’s box) or they obviously tried to get hit by the pitch
(regardless of its location)

(Reminder, the batter's hands are NOT considered part of the bat)

[M T]

Top of the seventh, two outs, two strikes on the batter. Umpire decides that the batter was hit by a pitch. Watching slow motion replays for I don’t know how many times it looks to me like it hit the bat.

The ump has one thing we don't: sound.  The ump signals the ball struck her left forearm.  It couldn't hit there, but one question is, did it FIRST strike her left fingers while on the bat or did it first strike the base of the bat.
I don't know if a struck-by-pitch is reviewable, but I'm glad Stanford didn't ask for a review.  The video isn't clear on what it hit.

At 70mph, the ball travels 3.4 feet every 30th of a second.  I think this is the best view you'll get

I see a bit of the bat between the ball and the left hand. Whether  the ball is not yet to the bat or is already past the base of the bat seems impossible to know, or if the ball has already bounced off the base of the bat is likewise impossible to know.

To my mind, the movement of the bat that I see in the slow motion view from behind the pitcher makes me think it hit the bat.  But that is only an impression.

So, while I disagree with the call, the call would not be overturned.

There are details in the rules about where the ball and the batter are (presumably at the time of contact), For this pitch in the 7th inning, the ball appeared to be entirely in the batter's box (hence 11.13.1 applies)

However, for the 1st inning call where the Stanford batter was hit by a (called) ball that was not entirely in the batter's box, so 11.13.2 applies, Appendix A "Feet and Lines Chart" indicates "Batter at bat/ball contact" has a Permissible Position "within" (vs "in/on") the "batter's box". By the definition and the overhead view, she was within the batter's box. She did (and announcer agreed) make a move to avoid being hit. So, did the umpire make the right call?

The rule says "any part of the batter or their clothing while THEY are in the batter's box". It s not "while the batter is in the batter's box" but "any [touched] part of the batter is in the batter's box". Note that any of the touched part has to be in the batter's box, not all. The overhead view supports that the part of the ball furtherest from the plate (a part that did touch her) is outside the (outer line of) the batter's box. So, I think that call was correct also.

11.13.1 A batter is awarded first base when a pitch, neither swung at nor called a
strike, is entirely within the batter’s box and it strikes the batter or their clothing.
No attempt to avoid being hit by the pitch is required; however, the batter may
not obviously try to get hit by the pitch. (See Rule 11.13.3.1.)
11.13.2 A batter is awarded first base when a pitch neither swung at nor called
a strike touches any part of the batter or their clothing while they are in the
batter’s box, except as noted in Rule 11.13.3 that follows.
11.13.3 The hit batter shall not be awarded first base under the following
circumstances:
11.13.3.1 The batter made no attempt to avoid the pitch (which is not
entirely in the batter’s box) or they obviously tried to get hit by the pitch
(regardless of its location)

(Reminder, the batter's hands are NOT considered part of the bat)