2013 Suburban LT, Z71, 133k: No engine light, old/stored codes P0700 P0741 P0742, transmission seems to shift perfectly smooth, no shuddering or slipping… any thoughts? Full details below:

I have been a long-time Tahoe/Suburban enthusiast/owner, and I have been patiently shopping for months for a 2011-2015 z71 suburban to add to the stable. Finally found one that is a southern-based truck with a good car fax, 130k miles, it was a recent trade at a large chevy dealership, I got to it early so no tune up or clean-up/conditioning yet. It ran seemingly great, everything I tested operational, engine fired up and idled perfectly smooth, no clunking U joints or engine mounts, transmission shifted smooth, no vibrations, no alignment pulls, interior in above average shape, drove it for about 25 minutes, 4wd engaged without any apparent issue. The dealership was seemingly honest and showed me the mechanics report from where their shop just checked it today - their list included a misfire code that they cleared up by cleaning the plugs up. Said had a pretty good oil drip; rear main seal oil leak. Needed front pads and rotors; brakes were a tad soft but not horrid. Unfortunately also had the P0700 P0741 and P0742 codes - transmission TCM and torque converter related. These are what I am most concerned with and looking for input on. The dealership manager said he was surprised to get the report from the shop as there was no check engine light and seemed to shift and run fine for them when they took the trade; he indicated they were “old codes”. The dealership was willing to work with me to fix all of the list, or leave some unfixed and improve the price for me. He said if I didn’t work something out with them their plan would most likely be to drive the vehicle for 50-100 miles to see if the transmission codes reappear or any evidence of an issue manifests, and they said most likely if they were unsure about it they’d likely choose to just take it to auction and sell it wholesale; so if that was the case they’d also be willing to work out selling it to me instead. They came across fairly sincere and thorough; they certainly didn’t need to tell me about the codes at all as the engine light was off and the vehicle drove seemingly fine.

I’ve been searching the forums and elsewhere for examples of seeing these codes even when the transmission is operating seemingly fine and haven’t found any strong examples. Anyone have any thoughts or input here? I suppose it is possible the previous owner had issues and replaced the torque converter solenoid already, or simply had low or poor ATF they replaced/filled and the issue cleared, and the codes are old/leftover from then. (Albeit this maybe is overly optimistic)

Any thoughts/inputs here? Any suggestions on how to test further or any experience with worst case / best case scenarios?

The only thing I can think of is return Monday and request to start the engine cold, drive it for 100 miles or so, with the transmission temp output displayed on the dash, and monitor for drive-ability issues and then check the codes after the drive. (I ran out of daylight/time today so was not able to check the actual transmission fluid to give it an eyeball-examination, so I will do that as well)

Any and all input/help is greatly appreciated.