Your pulley attached to the drum usually consists of a central hub fastened to the mounting shaft via bearings, the external surface having grooves for the driving belt. These are usually joined by ribs or spokes, and are rarely solid.
A waterproof hall effect switch mounted adjacent to the pulley should be able to sense these passing ribs. If the pulley is solid, epoxy two small magnets on opposite sides of the shaft [for balance to prevent vibration], and sense those by reed switch or hall effect transistor as your pulse input sensor.
If your rotation speed is once every five seconds, you will get a pulse every 2.5 seconds with two magnets, easy enough to detect with timing routines as falling within an 2 to 3 second window, and a timer reset routine that falls through if a pulse doesn't arrive within, say 10 seconds, and triggers the alarm routine (a watchdog timer condition). Within your main loop, keep track of a status flag that is examined on a regular basis for sending home 'all is well' data reports. Increment the counter each loop, and when it exceeds a fixed number of loops, send the 'all is well' alert and reset it. If your pulley has three spokes and you are detecting the spokes passing a hall effect transistor or reed switch, you will get three pulses every rotation. Adjust your timing loops appropriately.
MQTT may be an option for alerts. This will work over WiFi, ZigBee, LoRa, RS485, or whatever other networking option you choose to get your data back to your HomeAssistant server.
ESPHome, Tasmota, Arduino, or straight C or Micropython can all probably do the job on a firmware level. Lots of sample code related to water/gas meter pulse sampling will offer ideas you can get clues from. Beware that asking AI bots (ChatGPT, Claude, Copilot etc) for help with coding can often give you a confusing mishmash of hallucinations, obsolete or non-functional code.
Waterproof and climate tolerant case obligatory. Be aware if fully enclosed, there may be temperature rises for working electronics, and if externally mounted, subject to issues such as burning sun, rain, snow, corrosive sewage and other conditions.
12v7ah alarm batteries are cheap and readily available, and can be float charged for long life standby purposes for the sensor and alarm/alert circuits. Use a 2amp car adapter as your 12v to 5v stepdown power supply should be fine. Combine that with a cheap relay board, external flashing light and siren and you have most of your hardware taken care of.
Mounting inside a metal pit, or metallic case can mask your wireless signals. Read up about "Faraday Cage". You may need to run to an external antenna.
No smell detector necessary!!!