I have an AstroAI WH5000A also, Ill have to check the images on my desktop to fully confirm but the board layouts look almost exactly the same (i think yours is missing a sot-89 footprint that is unpopulated on mine, so they may have revised at some point and remove it). Except mine has a marked DM1106EN chip.
I also followed that blog to do exactly the same as you wanted (data output, lengthen the backlight timeout, and auto off time). While the backlight time, and auto off time was able to be changed on mine, the data output setting did not.
My best guess is either this chip physically does not support that feature, the feature was disabled at the factory (by blowing an E-fuse or something, since the chip supports pin muxing on some pins I imagine they have some facility to disable certain modes at the bare metal level), the activation is a different set of contacts (not entirely sure what the 6 extra pins near the fuses do, possibly some extra shenaniganery involving them is required, i don't know havent gotten that far yet), the data is on another pin (there are some oddities in the chip mentioned in the blog, the one dm1106 datasheet I was finally able to find, and the actual in device layout, nothing drastic, just...odd, like the test/reset pin on thr far side of the main IC being connected to one of the programming pins or something on the EEPROM side of the main IC), or any mixture of above and yet to be discovered voodoo. There are also the, what I believe are, SPI pins on the longer unpopulated (the two traced that go around the i2c header nearest the EEPROM to the IC a few pins down that might be worth taking a look at. I believe the last pin below those 2 is connected to the beeper circuit. I have been able to get the thing to start printing a series of hex strings on the screen, I cant remember how...as its my only meter ATM Im not keen on potentially bricking it, I did A LOT of research on what settings to change and how and writing them back to the chip before actually taking the leap. But there for sure are ways to get the IC into not-multimetery modes (it could just be a test mode but I dont have documentation that covers that).
Question: when you turn yours on and does the screen test in the upper left corner does yours have a "USB" or something else?
Ive noticed data output capable ones seem to say serial or some such, but mine says USB...IDK may indicate the data port it expects to expose once the right setting and button press is discovered (IIRC on the data sheet pins 14 and 15 were a EUART port on a similar chip or something. Again id have to check what I have in that project folder on my computer. Ill update when I do...).
Other than whatever they changed to make the data output not work, and the odd viewing angle of the LCD (its certainly not ment to be viewed dead on), its been a pretty decent meter. Like, yeah its cheap, sure it might not be perfectly accurate, and its definitely kinda slow, but its close enough to not blow anything, sturdy enough to get dropped a few times, and gets the job done. For the $30 or whatever I got it for (plus pouch, extra cables, K type thermocouple and accessories) Ive gotten my money's worth and more. Totally dont regret the purchase.