The most hardcore timepieces I ever had to use were the $50K+ clocks used in TV production galleries back in the olden days. These sent a time signal around the facility and there was usually a backup clock in a different part of the building, with both clocks talking to each other from the comfort of their respective 1U enclosures in 19" racks.
What I particularly liked was that these clocks did not actually tell you the time unless you hooked them up to your notebook's RS232 port and telneted in. We don't even have serial ports now, particularly on laptops, but I had to telnet into them to update them when the clocks changed to/from GMT/BST.
Up the road from these expensive clocks was a college that had a horology course. People on it would spend their three years making these absurd timepieces that were all about the mechanism and it was almost a point of pride for the students to have just an hour hand rather than something actually useful.
I feel that this watch concept needs a few more iterations to make it stylishly useless. For example, if the strap was like one of those ribbon cables we used to use to connect disk drives to the motherboard in early PCs, with an adaptor so the ribbon cable is either a watch strap, plugged into the watch, or a connector to a break out box that connects to a PC via USB, with this being the sole means of adjusting the watch or setting what mode it is in.
Regarding the screen and the terminal styling, this doesn't quite work for me as 'time' is what I type into the terminal to time something and 'date' is what I type in to get the date. I therefore see the terminal styling as a bit over the top. What I would like to see is an OG font from the 8 bit days, with blinking cursor, in old school LCD, think of the one character high screens that the last of the typewriters had.
Regarding changing the mode, some dip switches could come in handy. I think that there is fun to be had and that everyone would want to critique whatever gets made, as, ultimately, a CASIO is far better for the task in hand, plus you can also get calculator watches by them that get 90% of the aesthetic for a bargain price. But that is not the point though, much like the horology students, it is all about creating a timepiece and the challenges that involves, notably keeping the time accurate.
A for effort, and A for posting your work for armchair experts like me to critique!