I am facing exactly the same issue at the moment. I do not have much soldering experience but a friend of mine looked over my build and also measured the pins with a multimeter and an oscilloscope. Without looking into the exact signals, all of the pins (VCC, ground, SCL, SCA) seemed to be doing roughly what they are supposed to. Nevertheless, I am attaching some photos of my build for you to review.
When I am looking into my ESPHome logs, I see the following related to the SHT:
[20:10:05][C][i2c.arduino:037]: I2C Bus:
[20:10:05][C][i2c.arduino:038]: SDA Pin: GPIO4
[20:10:05][C][i2c.arduino:039]: SCL Pin: GPIO5
[20:10:05][C][i2c.arduino:040]: Frequency: 50000 Hz
[20:10:05][C][i2c.arduino:043]: Recovery: bus successfully recovered
[20:10:05][I][i2c.arduino:053]: Results from i2c bus scan:
[20:10:05][I][i2c.arduino:059]: Found i2c device at address 0x3C
<...>
[20:10:06][C][sht3xd:034]: SHT3xD:
[20:10:06][C][sht3xd:035]: Address: 0x44
[20:10:06][E][sht3xd:037]: Communication with SHT3xD failed!
[20:10:06][C][sht3xd:039]: Update Interval: 30.0s
[20:10:06][C][sht3xd:041]: Temperature 'Temperature'
[20:10:06][C][sht3xd:041]: Device Class: 'temperature'
[20:10:06][C][sht3xd:041]: State Class: 'measurement'
[20:10:06][C][sht3xd:041]: Unit of Measurement: '°C'
[20:10:06][C][sht3xd:041]: Accuracy Decimals: 1
[20:10:06][C][sht3xd:042]: Humidity 'Humidity'
[20:10:06][C][sht3xd:042]: Device Class: 'humidity'
[20:10:06][C][sht3xd:042]: State Class: 'measurement'
[20:10:06][C][sht3xd:042]: Unit of Measurement: '%'
[20:10:06][C][sht3xd:042]: Accuracy Decimals: 1
So in my (limited) understanding, the D1 Mini does not find the SHT although there is at least are some signal going through the I2C bus according to my friend’s measurements. The I2C device on 0x3C is the display.