Bootloop/wifi connection issues with illegal instruction exception, mostly on Sonoff devices

### The problem

There's been an influx of issues about Sonoff devices bootlooping/being unable to connect to wifi since v1.19 or v1.20. To save me and you from having to look a lot of issues, I want to centralize the discussion here.

If you have these symptoms, please:
* Obtain the full logs over the serial port, either using the `esphome logs` command or the dashboard.
* Check if there's an "Exception (0)" message in the output. If not, you don't have _this_ problem, please open a **new** issue.

If you have this issue, it'd be appreciated if you can try the following things and report back whether any of this solves or doesn't solve the problem:
* If you upgraded from a version prior to v1.18, check whether v1.18 works.
* If you upgraded to a version beyond v1.19, check whether v1.19 works.
* If you have set `arduino_version` under `esphome`, try it without.
* If you have set `esp8266_restore_from_flash` under `esphome` in your YAML, try disabling it.
* Try setting `level: INFO` under `logger` in your YAML.
* Try setting `enable_mdns: false` under `wifi` in your YAML (note that this may break the online/offline status in the dashboard, but the device itself should work fine).
* If you have it enabled, try disabling the captive portal.

Please include the following information in your reply:
* The exact make & model of your board
* The RAM/flash usage size reported during compilation
* The full serial output you obtained, **between \ and \ tags**.
* The *full* YAML you're using, **between \ and \ tags**.

### Which version of ESPHome has the issue?

v1.19 or v1.20

### Board

Mostly Sonoff / Shelly (possibly ESP8285-only?)

### Reports

Full reports:
* https://github.com/esphome/issues/issues/2210#issuecomment-879408817
* https://github.com/esphome/issues/issues/2198#issuecomment-895799321

Other reports:
* https://github.com/esphome/issues/issues/2210#issuecomment-871642613 (no stack decoded)
* https://github.com/esphome/issues/issues/2198#issue-930908877 (no stack decoded)
* https://community.home-assistant.io/t/esphome-device-wont-connect-to-wifi-after-upgrading-to-1-20-4/327756
* Issues
* #2272
* #2243
* #2210
* #2205
* #2147