Hi,
such a project is in my backlog for years now, but only materialized in some hardware (TFT and eInk screens in various shapes and capabilities) on my workbench and a lot of research
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even if your criteria 13 is a no go for a micro controller platforms my plan is to start a esp32 / c++ project. I think the ESP32 (depending on the model) is capable of the task (400k+ RAM, 2-8MB PSRAM, WLAN (and LAN option), fast SPI and even parallel LCD interfaces up to 16bit). The STM32s with there huge range of models could fit in here to and I have an STM32F746 DISCO board in my collection
With the ESP32-WROVER modules there is a solid CPU base and I was waiting for a single board solution with an min 3.2" capacitive touch screen and a small form factor I was sure someone in China will produce (and some enthusiasts on tindie notorious out of stock) sooner or later
And here they are in 2021:
On my desk (4.7" epaper 540x960 pixels, 16 gray levels (no color 
strange touch option but some nicely placed buttons), battery options. Nice for a wireless on the desk mobile information display
On order: WT01-SC01 (3.5" tft 480x320, capacitive touch) 40 € Currently my favorite as it clicks a lot of checkmarks
on my wish list: WT-86-32-3ZW1 (320x320 tft nice case) 60€ (perhaps a goto solution a soon the foftware is ready)
and as a development platform a all in one dev board from espressif ESP32-S2-HMI-DevKit-1 ( 4.3-inch display with 800×480 resolution, I2C capacitive touch panel 16bit inferface!) 70€ (if I need a bigger screen)
So plenty of nice all in one hardware solutions now form 30-100€.
On the software side I'm following https://lvgl.io/ for a while now and beside the challenging setup I think it is a solid open source platform for a mcu dashboard. From the inferface side I plan to use MQTT / Homie as a base but create the network inferface plugable with websockets as an option.
BTW The modules form wireless-tag provides a LVGL based point and click development platform ( 8ms GUI Development Platform) but as may of these kinds of software I have my problems, this is why I don't like the nextion modules (mine is collecting dust somewhere)
Now I only have to find some time to give this a start (anyone interested in a collaboration feel welcome to contact me 
Enough for a morning post 
@BartButenaers : Only a little tip. Don't use the BME280! It is so inaccurate (designed as a incredible accurate pressure sensor but not environment sensor) It appears (after research) that it looses the factory calibration if the reflow limits are not met precisely resulting in a temperature offset of up to 3°C! (the adafruit lib has a calibration function but my last research showed that it does not effect humidity accuracy which depends on precise temperature values). I use a BME680 (great IAQ sensor and human/animal presence sensor!) or my favorite TI-HDC2080 designed for the task.
Another one for tablet users: I use the open source android app (GitHub - thanksmister/wallpanel-android: WallPanel is an Android application for Web Based Dashboards and Home Automation Platforms)
