Thanks everyone for all the helpful suggestions! Here are the results (TLDR is, a combination of Alastair Gott's, Marco Corvi's, and Garry Petrie's suggestions solved the problem):
Balázs Holl: I could not calibrate the first DistoX2 twice. Upon reinstalling TopoDroid, I could upload the 56 calibration shots exactly once, and I could download the calibration to exactly one time to one DistoX2.
Alastair Gott: I could change TopoDroid to switch between using different DistoX2s (not in calibration mode) and upload survey data from each of the DistoX2s.
Further evidence that the Bluetooth connection was working properly is that I can use the "Reset Bluetooth" menu to, for example, reset the Bluetooth, or turn on and off the laser on all three DistoX2s. I could also use the "Reset Bluetooth" menu in calibration mode to reset the Bluetooth or to turn on and off the laser, too. None of this made a difference.
Although I do not think there was a hardware problem with the DistoX2s (each worked and calibrated just fine with my former Samsung Note 8 tablet), they DistoX2s were built by Eric Steinberg (Virginia, USA) in 2019 or 2020, serial nos. 4443, 4710, and 4711.
Using TopoDroid to enter calibration mode (instead of doing it with the DistoX2 by pressing the CLEAR and SMART (underlined right triangle) buttons for two seconds) did not seem to have any effect.
Marco Corvi: The silly causes ("silent" DistoX2, DistoX2 not in CAL mode, TopoDroid set to use another DistoX2) were not applicable.
I'm not sure what reason 4 (the data packets having the wrong code) might mean, so I wasn't able to check if this was the cause or not.
The calibration shots were indeed calibration shots, as noted by "CAL 056" on the DistoX2 screen.
When I tried to download the 56 calibration shots into the new calibration in TopoDroid, the Bluetooth icon on the DistoX2 screen DID blink, just before the "Read 0 data (0 packets)" error message appeared in TopoDroid.
To address the "app device database and jit," I did "force stop" TopoDroid and clear the tablet cache (power down, enter Android recovery mode using the Volume-Up and Power keys together, scrolling to "wipe cache," Volume-Up and Power to accept "wipe cache"). However, this procedure alone did not work.
Alastair Gott, Marco Corvi, and Garri Petrie:
I used a combination of your suggestions, and it worked! Here is the combination of actions that got me back on track; I'm not sure if any one of them did the trick or it was the combination:
(a) reset Bluetooth in TopoDroid;
(b) forced stop of TopoDroid from Android Settings-Apps-TopoDroid;
(c) cleared the tablet cache (power down, enter Android recovery mode using the Volume-Up and Power keys together, scrolling to "wipe cache," Volume-Up and Power to accept "wipe cache");
(d) turn off the DistoX2;
(e) restart TopoDroid;
(f) turn on the DistoX2;
(g) reset Bluetooth again in TopoDroid.
And voila! Now I can calibrate multiple DistoX2s, one after another, just like normal!
THANK YOU ALL! --Bert Ashbrook