For Cat-M1 and likely also NB-IoT there is not really a correlation between data rate and signal strength unless you are at very low signal strengths (like 1-bar equivalent). Note when signal strenght is poor it is also quite variable so you might have -110dBm signal one second and -130dBm the next second so even if this did correlate with speed at the low end, the measurement would be noisy and estimation unreliable. Also RSRQ is likely a better estimation than signal strength, again only relevant when both are low.
Data rate is mostly limited by the underlying technology (1Mb-379kb/s for Cat-M1, ~50kb/s for NB-IoT). I would also suspect other issues such as latency (can be quite high on IoT based tech) and its affects on TCP or your overall speed estimation if payload is small.
In summary, I dont think Cat-M1 or NB-IoT are good technology choices if reliable bandwidth is needed. These are more fit for periodic “heartbeat” like messages. Or non realtime applications where if a message takes 4s vs 0.4s to transmit it doesn’t really matter.
If you need performance closer to wifi / mobile phones then look at LTE-1, 2, 4, etc. modems.