Looks like the 8088 coprocessor board as in the Kaypro 4/84 Plus 88:
http://q7.neurotica.com/Oldtech/Kaypro/Kaypro488.html
The board was made by SWP Microcomputer Products, and available for several other systems:
https://retrocmp.de/kaypro/1985-08-20_SWP-Co-Power-88_kay_OCR.pdf
A bunch of Tandy experts, including people who designed hardware and wrote Xenix drivers for the big Tandys hang out on the Tandy Discord:
https://discord.gg/gy8GAkGJ
Your first system in an "Executive-style" case is actually the second version of the Osborne 1, often called the Osborne 1A. The Executive had 1/2-height drives on the left side of the CRT.
http://q7.neurotica.com/Oldtech/Osborne/Executive1L.jpg...
David:
I have the Lornes-special-osborne-software.zip file. I'll send you a DM.
The Computer History Museum has a schematic for the Screen-Pac:
https://www.computerhistory.org/collections/catalog/102665657
You could try contacting Al Kossow at Bitsavers to see if he has it scanned.
If you power up the Model 4 with no diskette inserted, or just press the RESET button with no diskette, it won't display anything. If you hold the BREAK key while doing a RESET, it should start up BASIC and you'll see text on the screen. You could ask the seller to try it.