Honestly sounds like a job for a Raspberry Pi Zero.
Small battery pack and a USB key, a bit of software setup, off you go.
Install Raspbian: https://www.raspberrypi.com/documentation/computers/getting-started.html#raspberry-pi-imager
Set it up as a hotspot:
https://www.raspberrypi.com/documentation/computers/configuration.html#enable-hotspot
Configure Samba share:
https://www.raspberrypi.com/documentation/computers/remote-access.html#samba
I can’t think of a standalone gui app that does this (and a simple google search didn’t find one).
If you have a gui desktop (gnome,kde,xfce,lxqt,enlightenment,budgie…) it will have a built in function in it’s settings to do this, or leverage one of the parent ones (ie budgie is based on gnome, lxqt on kde).
If your custom environment is pared down to the point where you don’t have an equivalent to gnome-system-tools and don’t want to install it, you might have to just use date at the command line.