MQTT is a great choice if the application requires the following:
Transmission of data between devices or from device to a server
Reliability of data transfer
Capability to scale
Compatibility with low-power devices
Robust for unreliable Internet connections
It sounds like your application has these requirements and that MQTT would be a sufficient solution....
MQTT is a good choice for you to send the sensor data to the central server. It is light weight and scalable. You can consume the data directly from a web interface or store it in a database. You can use node-red for creating streaming pipelines and visualizations
While you've said you're not looking for a general solution but you are probably going to end up using an SDR (Software Defined Radio).
While there are USB 915Mhz receivers (e.g. https://www.aliexpress.com/i/32378710247.html) they cost the same as basic receive only SDR capable hardware (https://www.nooelec.com/store/sdr/sdr-receivers/nesdr/nesdr-smart-sdr....
Having the right size capacitor matters. Especially if you used a different technology (i.e, you used electrolytic instead of ceramic). Ceramic is much better at filtering out high frequency noise. The electrolytic is good at filtering out brownouts due to sudden spikes in demand.
Also, make sure that you have a clean common ground. Try powering the sensor ...