Dear Sir,
we can use Nordic NRF52840 for main controller, as they are very popular on their bluetooth based microcontroller, and There is available arduino core for it, so it will be easier to program it's OLED display. For Lipo Charging, we can use TP4054 . It's simple charging IC that used on NodeMCU board. The package is small but it's enough for your application regarding that you have very small dimensions.
For your application, I think the issue following will be about battery, and antenna design, which is common issue for Bluetooth based device IoT.
I have became PCB designer since 2012 and has done Lot of project for various application, from hobbyst, Robotic, Industrial, IoT, Audio, until Military. I know how to analyze circuit, as well as program it, because my basic is Electronics Engineer and I work as both Electronic designer and firmware programmer since that that time.
I will use Eagle for this project. I will go with 2 layer first, but if it's not possible I will use 4 layer.
Let me know your response about my proposal. Just message me over chat. I have developed similar circuit before, with Nordic based microcontroller, on board antenna, LiPo Charging, and Epaper display,So I know how to manage it as well.
Best Regards,
Rijal