I have 13 ESP32's around the house and in the yard. They all send info to my RaspberryPi running MQTT Broker. I then, using the RPi, store the data in a Db and display the data on various displays and on my website. Also Node-Red can be used as a command/control center.
You can use a Mega connected to the LCD. The Mega has three additional UARTs for connection with other devices.
You can use RS485 and let the Arduino that has the LCD poll other devices.
You can use an Arduino that can act as a webserver for multiple connections; LCD connected to that. I'm not sure which Arduino/ESP can handle multiple concurrent connections. The other devices can connect as web clients.
Suppose a single arduino mini or nano is working as humidity sensor
Another one is working as proximity sensor
Third one is for a battery level indicator
Next one for a clock time with date in short
One more for IR Sensor
And here all the pins for boards are engaged due to some reason and only 2 pins for I2C left here for LCD Display
Now how to get them on single track to show multiple values from multiple device on a single display
A IR sensor + battery level + clock + I2C display + humidity + proximity sensor + IR sensor on a single Arduino board is no problem, assuming that the proximity sensor has a I2C bus.
One Arduino board : Good
Multiple Arduino boards : Often a bad idea
Your project with multiple Arduino boards : You just entered the clown mode
(I rewrote this post after reading the last update)
What type arduino boards are you using?
How far apart are the boards?
The major problem is getting the data into a single board, once that is done the display is fairly trivial.
Please tell why you need multiple boards.
Are you planning universal blocks that connect and disconnect ? The I2C bus is not plug and play. Then you would need serial communication. The block with the display should have its own Arduino board as others already wrote.
We are still trying to understand why you want to make it so hard for yourself to aim for something that might not be possible and does not seem to solve a problem.
All the ESP32's I have, 13 of them, use WiFi to transfer their data to a central unit. From there the central unit sends the info to the ESP'32 that have displays. MQTT Broker can be ran on a PC. Node-Red can be ran on a PC.
Seems hardware selection is an important consideration.